기탄수학 L1 답지 정답

L단계 교재 ①

1~60

정답및풀이

※ 정답 및 풀이는

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�

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L - 1 ( 1 )2, 3 ( 2 )57 ( 3 )3, 5 ( 4 )

a

8 ( 5 )

x

4 ( 6 )

x

9 ( 7 )

y

6 ( 8 )

y

10 ( 9 )3, 6 (10)711 ₍₁₁₎ 4, 9 (12)

a

11 (13)

b

8 (14)

b

9 (15)

x

7 (16)

x

10 (17)

y

5 (18)

y

12 <풀이> ※

x

m×

x

n ※=(`

x

×

x

×…×

x

)×(`

x

×…×

x

) ※=

x

×

x

×

x

×…×

x

※=

x

m+n ( 1 )지수가 없는 것처럼 보일 때에는‘`1’이 생략 된 것이다. 즉, 3은 31 에서 1을 생략하고 나타 낸 것으로, 이것은

x

×1을 1

x

가 아니고

x

로 나타내는 것과 같다. 3×32 =31+2 =33 ( 2 )52 ×55 =52+5 =57 ( 3 )

a

3×

a

2=

a

3+2=

a

5 ( 4 )

a

2×

a

6 =

a

2+6 =

a

8 ( 5 )

x

2×

x

2 =

x

2+2 =

x

4 ( 6 )

x

6×

x

3 =

x

6+3 =

x

9 ( 7 )

y

5×

y

=

y

5+1 =

y

6 ( 8 )

y

3×

y

7 =

y

3+7 =

y

10 ※

x

l×

x

m×

x

n=(

x

l×

x

m)×

x

n =

x

l+m×

x

n =

x

l+m+n ( 9 )2×22 ×23 =21+2+3 =26 <다른 풀이> 2×22 ×23 =21+2 ×23 =23 ×23 =23+3 =26 (10)74 ×75 ×72 =74+5+2 =711 (11)

a

4×

a

3 ×

a

2 =

a

4+3+2 =

a

9 <다른 풀이>

a

4 ×

a

3 ×

a

2 =

a

4+3 ×

a

2 =

a

7 ×

a

2 =

a

7+2 =

a

9 (12)

a

2×

a

3 ×

a

6 =

a

2+3+6 =

a

11 (13)

b

3×

b

2 ×

b

3 =

b

3+2+3 =

b

8 (14)

b

3×

b

3 ×

b

3 =

b

3+3+3 =

b

9 (15)

x

2×

x

3 ×

x

2 =

x

2+3+2 =

x

7 (16)

x

5×

x

2×

x

3=

x

5+2+3=

x

10 (17)

y

2×

y

2 ×

y

=

y

2+2+1 =

y

5 (18)

y

3×

y

4 ×

y

5 =

y

3+4+5 =

y

12 L - 2 ( 1 )1, 4 ( 2 )28×52 ( 3 )2, 6, 6 ( 4 )

a

4

b

10 ( 5 )

a

7

b

7 ( 6 )

x

5

y

2 ( 7 )

x

6

y

9 ( 8 )

x

8

y

5 ( 9 )1, 6, 3, 8 (10)37 ×45 ₍₁₁₎ 4, 11, 11 (12)

a

4

b

9 (13)

a

10

b

7 (14)

x

15

y

4 (15)

x

12

y

6 (16)

x

8

y

11 <풀이> ※

x

l×

y

m×

x

n=

x

l×

x

n×

y

m =

x

l+n×

y

m =

x

l+n

y

m ( 1 )지수법칙

a

m×

a

n=

a

m+n은 두 수의 밑이 같은 경우에만 쓸 수 있다. 즉, 34 ×75_{은 더 이상 간단히 할 수 없다.} ( 2 )24 ×24 ×52 =24+4 ×52 =28 ×52 ( 4 )

a

4×

b

2 ×

b

8 =

a

4 ×

b

2+8 =

a

4 ×

b

10 =

a

4

b

10 ( 5 )

a

4×

b

7 ×

a

3 =

a

4 ×

a

3 ×

b

7 =

a

4+3 ×

b

7 =

a

7 ×

b

7 =

a

7

b

7 ( 6 )

x

4×

x

×

y

2 =

x

4+1 ×

y

2 =

x

5 ×

y

2 =

x

5

y

2 ( 7 )

x

6×

y

5 ×

y

4 =

x

6 ×

y

5+4 =

x

6 ×

y

9 =

x

6

y

9 ( 8 )

x

×

y

5 ×

x

7 =

x

×

x

7 ×

y

5 =

x

1+7 ×

y

5 =

x

8 ×

y

5 =

x

8

y

5 ※

x

k×

y

l×

x

m×

y

n=

x

k×

x

m×

y

l×

y

n =

x

k+m×

y

l+n =

x

k+m

y

l+n (10)32 ×42 ×43 ×35 =32 ×35 ×42 ×43 =32+5 ×42+3 =37 ×45 (12)

a

×

a

3 ×

b

8 ×

b

=

a

1+3 ×

b

8+1 =

a

4 ×

b

9 =

a

4

b

9 (13)

a

5×

b

×

a

5 ×

b

6 =

a

5 ×

a

5 ×

b

×

b

6 =

a

5+5 ×

b

1+6 =

a

10 ×

b

7 =

a

10

b

7 (14)

x

4×

x

5 ×

x

6 ×

y

4 =

x

4+5+6 ×

y

4 =

x

15 ×

y

4 =

x

15

y

4 (15)

x

9×

y

×

y

5×

x

3=

x

9×

x

3×

y

×

y

5 =

x

9+3 ×

y

1+5 =

x

12 ×

y

6 =

x

12

y

6 (16)

x

3×

y

4 ×

x

5 ×

y

7 =

x

3 ×

x

5 ×

y

4 ×

y

7 =

x

3+5×

y

4+7 =

x

8 ×

y

11 =

x

8

y

11 ( \ { \ 9

_m

_개 ( ₍\

_m

₊

_n

{_)개\ 9 (

_n

_개{ 9

3~5

L-1

정답및풀이

L - 3 ( 1 )3, 6 ( 2 )78 ( 3 )3, 12 ( 4 )

a

4 ( 5 )

x

14 ( 6 )

x

9 ( 7 )

y

6 ( 8 )

y

10 ( 9 )3, 3, 15 (10)

a

12 (11)

x

21 (12)4, 8, 11 (13)

b

13 (14)

y

16 (15)312 (16)

a

22 (17)

x

25 (18)

y

21 <풀이> ※ (

x

m)n=

x

m×

x

m×

x

m×…×

x

m ※ (

x

m)n=

x

m+m+m+…+m ※ (

x

m)n=

x

m×n ※ (

x

m)n=

x

mn ( 1 )(22)3=22×3=26 ( 2 )(74 )2 =74×2 =78 ( 3 )(

a

3 )4 =

a

3×4 =

a

12 ( 4 )(

a

2 )2 =

a

2×2 =

a

4 ( 5 )(

x

7 )2 =

x

7×2 =

x

14 ( 6 )(

x

3)3=

x

3×3=

x

9 ( 7 )(

y

3 )2 =

y

3×2 =

y

6 ( 8 )(

y

2 )5 =

y

2×5 =

y

10 ( 9 )_지수법칙

x

m×

x

n=

x

m+n을 이용하여 간단 히 한 후, 지수법칙 (

x

m)n=

x

mn을 이용한다. (7×72)5=(73)5=73×5=715 (10)(

a

3 ×

a

3 )2 =(

a

6 )2 =

a

6×2 =

a

12 (11)(

x

2 ×

x

3 ×

x

2 )3 =(

x

7 )3 =

x

7×3 =

x

21 (12)_{지수법칙 (}

x

m)n=

x

mn을 이용하여 괄호를 푼 다음, 지수법칙

x

m×

x

n=

x

m+n을 이용 하여 간단히 한다. (52 )4 ×53 =52×4 ×53 =58 ×53 =511 (13)

b

×(

b

4 )3 =

b

×

b

4×3 =

b

×

b

12 =

b

13 (14)(

y

2 )6 ×(

y

2 )2 =

y

2×6 ×

y

2×2 =

y

12 ×

y

4 =

y

16 (15)(33 )2 ×34 ×32 =33×2 ×34 ×32 =36 ×34 ×32 =312 (16)

a

×(

a

2 )3 ×(

a

5 )3 =

a

×

a

2×3 ×

a

5×3 =

a

×

a

6×

a

15 =

a

22 (17)(

x

2 )5 ×(

x

5 )2 ×

x

5 =

x

2×5 ×

x

5×2 ×

x

5 =

x

10 ×

x

10 ×

x

5 =

x

25 (18)(

y

3)3×(

y

4)2×(

y

2)2=

y

3×3×

y

4×2×

y

2×2 =

y

9 ×

y

8 ×

y

4 =

y

21 L - 4 ( 1 )2, 6 ( 2 )35×718 ( 3 )2, 18 ( 4 )

a

8

b

20 ( 5 )

a

12

b

7 ( 6 )

x

2

y

16 ( 7 )

x

9

y

4 ( 8 )

x

14

y

20 ( 9 )2, 4, 7 (10)313 ×514 ₍₁₁₎ 2, 10, 16 (12)

a

18

b

16 (13)

a

20

b

10 (14)

x

2

y

23 (15)

x

21

y

32 (16)

x

26

y

18 <풀이> ( 2 )35 ×(73 )6 =35 ×73×6 =35 ×718 ( 4 )(

a

2 )4 ×(

b

4 )5 =

a

2×4 ×

b

4×5 =

a

8

b

20 ( 5 )(

a

4 )3 ×

b

7 =

a

4×3 ×

b

7 =

a

12

b

7 ( 6 )

x

2×(

y

8 )2 =

x

2 ×

y

8×2 =

x

2

y

16 ( 7 )(

x

3 )3 ×

y

4 =

x

3×3 ×

y

4 =

x

9

y

4 ( 8 )(

x

7 )2 ×(

y

5 )4 =

x

7×2 ×

y

5×4 =

x

14

y

20 (10)(34 )2 ×35 ×(52 )7 =34×2 ×35 ×52×7 =38 ×35 ×514 =313 ×514 (12)(

a

3 )4 ×(

b

4 )4 ×(

a

2 )3 =

a

3×4 ×

b

4×4 ×

a

2×3 =

a

12 ×

b

16 ×

a

6 =

a

18

b

16 (13)(

a

6 )3 ×

b

3 ×

a

2 ×

b

7 =

a

6×3 ×

b

3 ×

a

2 ×

b

7 =

a

18 ×

b

3 ×

a

2 ×

b

7 =

a

20

b

10 (14)

x

×(

y

2 )4 ×(

y

5 )3 ×

x

=

x

×

y

2×4 ×

y

5×3 ×

x

=

x

×

y

8 ×

y

15 ×

x

=

x

2

y

23 (15)(

x

2 )6 ×(

x

3 )3 ×(

y

7 )4 ×

y

4 =

x

2×6 ×

x

3×3 ×

y

7×4 ×

y

4 =

x

12 ×

x

9 ×

y

28 ×

y

4 =

x

21

y

32 (16)(

x

8 )2 ×(

y

2 )3 ×(

x

5 )2 ×(

y

4 )3 =

x

8×2 ×

y

2×3 ×

x

5×2 ×

y

4×3 =

x

16 ×

y

6 ×

x

10 ×

y

12 =

x

26

y

18 ( |

_n

_개{ | 9 ( \ { \ 9

n

개 L - 5 ( 1 )7, 3 ( 2 )1 ( 3 )5, 4 ( 4 )56 ( 5 )1 ( 6 ) ( 7 )

x

5 ( 8 ) ( 9 )3, 6, 6, 2 (10)5, 3, 1 (11)5, 2, 2, 4 (12)

a

(13)1 (14) (15)

x

2 (16)1 (17)

y

12 (18)

y

4 1

b

5 1

y

1

b

7

(18)

y

8÷

y

÷

y

3 =

y

8-1 ÷

y

3 =

y

7 ÷

y

3 =

y

7-3 =

y

4 L - 6 ( 1 )4, 1 ( 2 )6, 9, 3 ( 3 )15, 15, 7 ( 4 ) ( 5 )

x

2 ( 6 ) ( 7 )

y

4 ( 8 )1 ( 9 )12, 12, 10, 10, 4 (10) (11)1 (12)

a

(13) (14)1 (15)

y

4 (16) 1

y

10 1

x

8 1 33 1

x

2 1

a

7 <풀이> ※ 괄호가 있는 경우 가장 먼저 괄호를 풀어 준다. ( 4 )

a

5÷(

a

2 )6 =

a

5 ÷

a

12 = = ( 5 )(

x

5 )2 ÷

x

8 =

x

10 ÷

x

8 =

x

10-8 =

x

2 ( 6 )(

x

3 )2 ÷(

x

2 )4 =

x

6 ÷

x

8 = = ( 7 )(

y

6 )2 ÷

y

8 =

y

12 ÷

y

8 =

y

12-8 =

y

4 ( 8 )(

y

3 )4 ÷(

y

4 )3 =

y

12 ÷

y

12 =1 (10)313 ÷(33 )2 ÷(32 )5 =313 ÷36 ÷310 =313-6 ÷310 =37 ÷310 (10)313 ÷(33 )2 ÷(32 )5 = (10)313 ÷(33 )2 ÷(32 )5 = (11)

a

6÷(

a

2 )2 ÷

a

2 =

a

6 ÷

a

4 ÷

a

2 =

a

6-4 ÷

a

2 =

a

2 ÷

a

2 =1 (12)(

a

6 )3 ÷

a

9 ÷(

a

4 )2 =

a

18 ÷

a

9 ÷

a

8 =

a

18-9 ÷

a

8 =

a

9 ÷

a

8 =

a

9-8 =

a

1 33 1 310-7 1

x

2 1

x

8-6 1

a

7 1

a

12-5 <풀이> ※

x

m÷

x

n= ※

x

m÷

x

n= 에서 분모, 분자를 약분하면 �

m

>

n

일 때,

x

m-n �

m

=

n

일 때, 1 �

m

<

n

일 때, 즉,

x

m÷

x

n의 계산에서는

m

과

n

의 대소 관계 에 따라 그 지수가 달라진다. ( 4 )58 ÷52 =58-2 =56 ( 6 )

b

2÷

b

9= = ( 7 )

x

9÷

x

4=

x

9-4=

x

5 ( 8 )

y

5÷

y

6 = = ※ 나눗셈은 교환법칙이 성립하지 않으므로 왼 쪽부터 차례로 계산한다. (12)

a

8÷

a

4 ÷

a

3 =

a

8-4 ÷

a

3 =

a

4 ÷

a

3 =

a

4-3 =

a

(13)

b

8÷

b

3 ÷

b

5 =

b

8-3 ÷

b

5 =

b

5 ÷

b

5 =1 (14)

b

3÷

b

2÷

b

6=

b

3-2÷

b

6 =

b

÷

b

6 (14)

b

3÷

b

2 ÷

b

6 = (14)

b

3÷

b

2 ÷

b

6 = (15)

x

6÷

x

3 ÷

x

=

x

6-3 ÷

x

=

x

3 ÷

x

=

x

3-1 =

x

2 (16)

x

7÷

x

÷

x

6 =

x

7-1 ÷

x

6 =

x

6 ÷

x

6 =1 (17)

y

9÷

y

7 ÷

y

4 =

y

9-7 ÷

y

4 =

y

2 ÷

y

4 (17)

b

3÷

b

2 ÷

b

6 = (17)

b

3÷

b

2 ÷

b

6 =

_y

12 1

y

4-2 1

b

5 1

b

6-1 1

y

1

y

6-5 1

b

7 1

b

9-2 1

x

n-m

x

×

x

×

x

×…×

x

x

×

x

×

x

×…×

x

x

m

x

n ( \

_n

_개{ \ 9 ( \ { \ 9

m

개

6~8

L-1

정답및풀이

(13)(

x

5 )3 ÷(

x

3 )3 ÷(

x

2 )7 =

x

15 ÷

x

9 ÷

x

14 =

x

15-9 ÷

x

14 =

x

6÷

x

14 (13)(

x

5 )3 ÷(

x

3 )3 ÷(

x

2 )7 = (13)(

x

5)3÷(

x

3)3÷(

x

2)7= (14)

x

9÷

x

÷(

x

4 )2 =

x

9 ÷

x

÷

x

8 =

x

9-1 ÷

x

8 =

x

8 ÷

x

8 =1 (15)(

y

4 )4 ÷(

y

2 )3 ÷

y

6 =

y

16 ÷

y

6 ÷

y

6 =

y

16-6 ÷

y

6 =

y

10 ÷

y

6 =

y

10-6 =

y

4 (16)(

y

2 )8 ÷(

y

7 )2 ÷(

y

3 )4 =

y

16 ÷

y

14 ÷

y

12 =

y

16-14 ÷

y

12 =

y

2 ÷

y

12 (16)(

y

2 )8 ÷(

y

7 )2 ÷(

y

3 )4 = (16)(

y

2 )8 ÷(

y

7 )2 ÷(

y

3 )4 =

_y

110 1

y

12-2 1

x

8 1

x

14-6 L - 7 ( 1 )4, 4 ( 2 )2, 2, 6, 2 ( 3 )

a

5

b

10 ( 4 )

x

6

y

9 ( 5 )5, 5 ( 6 )3, 3, 3, 6 ( 7 ) ( 8 ) ( 9 )2, 2, 25, 6 (10)27

x

12 ₍₁₁₎ 6, 6,

b

12 ₍₁₂₎ 16

y

8 (13)-27

x

15 ₍₁₄₎ 5, 5, 10, 32(15) (16)3, 3, 12, -64, 12, 64 (17) (18)-

x

6 8 1

y

10 49

x

16

y

8

x

16

b

8

a

2 <풀이> ※ �(

xy

)n=

xy

×

xy

×…×

xy

=

x

×

x

×…×

x

×

y

×

y

×…×

y

=

x

n

y

n ※�& *n= × ×…× ※ �& *n ※ �& *n= ※ �& *n= ( 3 )(

ab

2 )5 =

a

5 (

b

2 )5 =

a

5

b

10 ( 4 )(

x

2

y

3 )3 =(

x

2 )3 (

y

3 )3 =

x

6

y

9 ( 7 )_{& *} 2 = = ( 8 )_{& *} 4 = = (10)(3

x

4 )3 =33 (

x

4 )3 =27

x

12 (11)‘`-`’가 들어 있는 거듭제곱을 간단히 할 때 에는 부호부터 결정하는 것이 편리하다. (-)n� (12)(-2

y

2 )4 =(-2)4 (

y

2 )4 =16

y

8 (13)(-3

x

5 )3 =(-3)3 (

x

5 )3 =-27

x

15 (15)_{& *} 2 = = (17)_{&- *} 2 = = (18)_{&- *} 3 = = =-

x

6 8

x

6 -8 (

x

2 )3 (-2)3

x

2 2 1

y

10 (-1)2 (

y

5 )2 1

y

5 49

x

16 72 (

x

8 )2 7

x

8 [

n

_n

이 짝수일 때：+ 이 홀수일

때：-y

8

x

16 (

y

2 )4 (

x

4 )4

y

2

x

4

b

8

a

2 (

b

4)2

a

2

b

4

a

x

n

y

n

x

×

x

×…×

x

y

×

y

×…×

y

x

y

x

y

x

y

x

y

L - 8 ( 1 )2, 2, 2,

a

2

b

4

c

6 ( 2 )

x

8

y

4

z

16 ( 3 )

a

6

b

9

c

12 ( 4 )

x

15

y

10

z

25 ( 5 )3, 3, 9, 3, 3, ( 6 ) ( 7 ) ( 8 ) ( 9 )2, 2, 2, 9

a

8

b

4 ₍₁₀₎ 16

x

18

y

2 (11)-32

a

5

b

15 ₍₁₂₎ 16

x

4

y

10 (13)4, 4, 4, 4, 12, (14) (15) (16)-

y

3 27

x

6

b

20

a

8

x

10 36

y

4 16

a

4

b

12

x

4

y

6

z

8

a

12

b

8

c

20

x

5

y

10

z

20

a

9

b

6

c

3 ( |

_n

_개{ | 9 ( | { | 9

_n

_개 ( | { | 9

n

개 ( |

_n

_개{ | 9 ( \ { \ 9

_n

_개 ( \ { \ 9

_n

_개

( 7 )₍

a

2₎4_×(

b

5₎2=

a

2×4 ×

b

5×2 ( 7 )(

a

2₎4_×(

b

5₎2 =

a

8

b

10 ( 8 )(

x

8 )3 ×(

y

4 )2 ×

y

3=

x

8×3×

y

4×2×

y

3 ( 8 )₍

x

8₎3_×(

y

4₎2×

y

3 =

x

24 ×

y

8 ×

y

3 ( 8 )₍

x

8₎3_×(

y

4₎2×

y

3 =

x

24

y

11 ( 9 )

a

11÷

a

4 =

a

11-4 =

a

7 (10)

x

7÷

x

2÷

x

5=

x

7-2÷

x

5=

x

5÷

x

5=1 (11)(

b

3₎2 ÷

b

12 =

b

6 ÷

b

12 = = (12)₍

y

6₎4_÷(

y

2₎6_÷(

y

4₎2=

y

24 ÷

y

12 ÷

y

8 (12)(

y

6₎4_÷(

y

2₎6_÷(

y

4₎2 =

y

24-12 ÷

y

8 (12)(

y

6 )4 ÷(

y

2 )6 ÷(

y

4 )2 =

y

12÷

y

8 (12)₍

y

6₎4_÷(

y

2₎6_÷(

y

4₎2=

y

12-8 (12)₍

y

6₎4_÷(

y

2₎6_÷(

y

4₎2=

y

4 (13)(

a

3

b

4₎4₌₍

a

3₎4₍

b

4₎4 =

a

12

b

16 (14)_{&- *} 2 = = (15)_{& *} 3 = = = (16)(2

x

3

y

)4 =24 (

x

3 )4

y

4 =16

x

12

y

4

c

6

a

3

b

15

c

6

a

3 (

b

5)3 (

c

2)3 (

ab

5)3

c

2

ab

5 9

y

10 (-3)2 (

y

5 )2 3

y

5 1

b

6 1

b

12-6 L - 9 ( 1 )

a

13 ( 2 )

x

16 ( 3 )

a

8

b

4 ( 4 )

x

9

y

11 ( 5 )

a

42 ( 6 )

x

22 ( 7 )

a

8

b

10 ( 8 )

x

24

y

11 ( 9 )

a

7 (10)1 (11) (12)

y

4 (13)

a

12

b

16 (14) (15) (16)16

x

12

y

4

c

6

a

3

b

15 9

y

10 1

b

6 <풀이> ( 1 )

a

8×

a

5 =

a

8+5 =

a

13 ( 2 )

x

2×

x

9 ×

x

5 =

x

2+9+5 =

x

16 ( 3 )

a

7×

b

4 ×

a

=

a

7 ×

a

×

b

4 =

a

7+1 ×

b

4 =

a

8

b

4 ( 4 )

x

3×

y

8 ×

y

3 ×

x

6 =

x

3 ×

x

6 ×

y

8 ×

y

3 ( 4 )

x

3×

y

8 ×

y

3 ×

x

6 =

x

3+6 ×

y

8+3 ( 4 )

x

3×

y

8 ×

y

3 ×

x

6 =

x

9

y

11 ( 5 )(

a

7₎6 =

a

7×6 =

a

42 ( 6 )

x

4×(

x

9 )2 =

x

4 ×

x

9×2 ( 6 )

x

4_×(

x

9₎2=

x

4 ×

x

18 ( 6 )

x

4×(

x

9₎2 =

x

22 L - 10 ( 1 )

a

3

b

9 ( 2 )

x

7

y

4

z

7 ( 3 )

a

17 ( 4 )

x

16

y

9 ( 5 ) ( 6 )1 ( 7 )32

a

15

b

10 _{( 8 )} - ( 9 ) (10)

x

6 (11) (12)1 (13)

a

12 (14)1 (15)

b

3 (16)

y

12 1

b

3 1

a

2 27

x

9

y

3

z

6 1

a

3 <풀이> ( 1 )

a

2×

b

4 ×

a

×

b

3 ×

b

2 =

a

2 ×

a

×

b

4 ×

b

3 ×

b

2 ( 1 )

a

2×

b

4×

a

×

b

3×

b

2=

a

2+1×

b

4+3+2 ( 1 )

a

2×

b

4 ×

a

×

b

3 ×

b

2 =

a

3

b

9 ( 2 )

x

×

y

3 ×

z

4 ×

y

×

z

3 ×

x

6 =

x

×

x

6 ×

y

3 ×

y

×

z

4 ×

z

3 =

x

1+6×

y

3+1×

z

4+3 =

x

7

y

4

z

7 ( 3 )(

a

3₎4_×(

a

2₎2 ×

a

=

a

3×4 ×

a

2×2 ×

a

( 3 )(

a

3₎4_×(

a

2₎2 ×

a

=

a

12 ×

a

4 ×

a

( 3 )(

a

3 )4 ×(

a

2 )2 ×

a

=

a

17 <풀이> ( 2 )(

x

2

yz

4 )4 =(

x

2 )4

y

4 (

z

4 )4 =

x

8

y

4

z

16 ( 3 )(

a

2

b

3

c

4 )3 =(

a

2 )3 (

b

3 )3 (

c

4 )3 =

a

6

b

9

c

12 ( 4 )(

x

3

y

2

z

5)5=(

x

3)5(

y

2)5(

z

5)5=

x

15

y

10

z

25 ( 6 )_{& *} 5 = = = ( 7 )_{& *} 4 = = = ( 8 )_{& *} 2 = = = (10)(4

x

9

y

)2=42(

x

9)2

y

2=16

x

18

y

2 (11)(-2

ab

3 )5 =(-2)5

a

5 (

b

3 )5 =-32

a

5

b

15 (12)(-4

x

2

y

5 )2 =(-4)2 (

x

2 )2 (

y

5 )2 =16

x

4

y

10 (14)_{& *} 2 = = = (15)_{&- *} 4 = = = (16)_{&- *} 3 = = = =-

y

3 27

x

6 -

y

3 27

x

6 (-1)3

y

3 33 (

x

2 )3 (-

y

)3 (3

x

2 )3

y

3

x

2

b

20

a

8 (-1)4 (

b

5 )4

a

8 (-

b

5 )4 (

a

2 )4

b

5

a

2

x

10 36

y

4

x

10 62 (

y

2 )2 (

x

5 )2 (6

y

2 )2

x

5 6

y

2

x

4

y

6

z

8

x

4 (

y

3 )2 (

z

4 )2 (

x

2 )2 (

y

3

z

4 )2

x

2

y

3

z

4

a

12

b

8

c

20 (

a

3 )4 (

b

2 )4

c

20 (

a

3

b

2 )4 (

c

5 )4

a

3

b

2

c

5

x

5

y

10

z

20

x

5 (

y

2 )5

z

20 (

xy

2 )5 (

z

4 )5

xy

2

z

4

10~11

L-1

정답및풀이

( 4 )₍

x

7₎2_×(

y

2₎3×

x

2 ×

y

3 =

x

7×2 ×

y

2×3 ×

x

2 ×

y

3 =

x

14 ×

y

6 ×

x

2 ×

y

3 =

x

16

y

9 ( 5 )

a

9÷

a

7 ÷

a

5 =

a

9-7 ÷

a

5 ( 5 )

a

9÷

a

7 ÷

a

5 =

a

2 ÷

a

5 ( 5 )

a

9÷

a

7 ÷

a

5 = ( 5 )

a

9÷

a

7 ÷

a

5 = ( 6 )₍

x

4₎4_÷(

x

2₎5_÷(

x

3₎2=

x

16 ÷

x

10 ÷

x

6 ( 6 )(

x

4₎4_÷(

x

2₎5_÷(

x

3₎2 =

x

16-10 ÷

x

6 ( 6 )(

x

4₎4_÷(

x

2₎5_÷(

x

3₎2 =

x

6 ÷

x

6 ( 6 )(

x

4 )4 ÷(

x

2 )5 ÷(

x

3 )2 =1 ( 7 )₍₂

a

3

b

2₎5=25 (

a

3 )5 (

b

2 )5 =32

a

15

b

10 ( 8 )_{&- *} 3 = ( 8 )_{&- *}3= ( 8 )_{&- *}3= ( 8 ) _{&- *}3 =-( 9 )

a

2×

a

3 ÷

a

7 =

a

5 ÷

a

7 = (10)

x

4÷

x

×

x

3 =

x

3 ×

x

3 =

x

6 (11)₍

b

2₎5×

b

2 ÷(

b

5 )3 =

b

10 ×

b

2 ÷

b

15 (11)(

b

2₎5 ×

b

2_÷(

b

5₎3 =

b

12 ÷

b

15 (11)₍

b

2₎5×

b

2 ÷(

b

5 )3 = (12)₍

y

3₎2_÷(

y

2₎4×

y

2 =

y

6 ÷

y

8 ×

y

2 (11)(

y

2 )5 ×

y

2÷(

y

5 )3 = ×

y

2 (11)(

b

2₎5 ×

b

2_÷(

b

5₎3 =1 (13)

a

4_×(

a

3×

a

5 )=

a

4 ×

a

8 =

a

12 (14)

x

×(

x

3 ÷

x

4₎₌

x

× =1 (15)

b

8÷(

b

×

b

4₎₌

b

8 ÷

b

5 =

b

3 (16)

y

2÷(

y

7 ÷

y

3₎₌

y

2 ÷

y

4 =

_y

12 1

x

1

y

2 1

b

3 1

a

2 27

x

9

y

3

z

6 -27

x

9

y

3

z

6 (-3)3(

x

3)3

y

3

z

6 (-3

x

3

y

)3 (

z

2 )3 3

x

3

y

z

2 1

a

3 1

a

5-2 L - 11 ( 1 )3, 3, 21 ( 2 )-30

xy

( 3 )-28

ab

( 4 )18

xy

( 5 )2, 2, 16 ( 6 )-36

x

3

y

( 7 )-54

a

2

b

3 _{( 8 )} 8

x

4

y

5 ( 9 )

a

,

a

,

a

5 (10)-9

x

8 (11)-20

b

10 ₍₁₂₎ 42

y

7 (13)9, 9, 27, 6 (14)-24

x

11

y

2 (15)-56

a

4

b

8 ₍₁₆₎ 15

x

9

y

5 <풀이> ※ 단항식의 곱셈에서는 먼저 각 항의 부호만을 계산하여 전체의 부호를 결정한 후 곱셈을 하면 편리하다. ( 2 )5

x

×(-6

y

)=5×

x

×(-6)×

y

( 2 )5

x

×(-6

y

)=5×(-6)×

x

×

y

( 2 )5

x

×(-6

y

)=-30

xy

( 3 )(-7

a

)×4

b

=(-7)×

a

×4×

b

( 3 )_(-7

a

_)×4

b

_=(-7)×4×

a

×

b

( 3 )_(-7

a

_)×4

b

=-28

ab

( 4 )_(-6

x

_)×(-3

y

_)=(-6)×

x

_×(-3)×

y

( 4 )(-6

x

)×(-3

y

)=(-6)×(-3)×

x

×

y

( 4 )(-6

x

)×(-3

y

)=18

xy

( 6 )4

x

3_×(-9

y

_)=4×

x

3_×(-9)×

y

( 5 )4

x

3_×(-9

y

_)=4×(-9)×

x

3 ×

y

( 5 )4

x

3_×(-9

y

₎ =-36

x

3

y

( 7 )(-9

a

2 )×6

b

3 =(-9)×

a

2 ×6×

b

3 ( 7 )(-9

a

3 )×6

b

3 =(-9)×6×

a

2 ×

b

3 ( 7 )_(-9

a

3_)×6

b

3=-54

a

2

b

3 ( 8 )_(-2

x

4_)×(-4

y

5_)=(-2)×

x

4_×(-4)×

y

5 ( 8 )_(-2

x

4_)×(-4

y

5_{)=(-2)×(-4)×}

x

4×

y

5 ( 8 )(-2

x

4_)×(-4

y

5₎ =8

x

4

y

5 (10)3

x

5_×(-3

x

3_)=3×

x

5_×(-3)×

x

3 (10)3

x

5_×(-3

x

3_)=3×(-3)×

x

5 ×

x

3 (10)3

x

5_×(-3

x

3₎ =-9

x

8 (11)(-4

b

4_)×5

b

6_=(-4)×

b

4 ×5×

b

6 (11)(-4

b

4 )×5

b

6 =(-4)×5×

b

4 ×

b

6 (11)(-4

b

4 )×5

b

6 =-20

b

10 (12)_(-7

y

2_)×(-6

y

5_)=(-7)×

y

2_×(-6)×

y

5 (12)(-7

y

2_)×(-6

y

5_{)=(-7)×(-6)×}

y

2 ×

y

5 (12)(-7

y

2_)×(-6

y

5₎ =42

y

7 (14)6

x

7 ×(-4

x

4

y

2 )=6×

x

7 ×(-4)×

x

4 ×

y

2 (14)6

x

7 ×(-4

x

4

y

2 )=6×(-4)×

x

7 ×

x

4 ×

y

2 (14)6

x

7_×(-4

x

4

y

2₎ =-24

x

11

y

2 (15)(-8

a

2

b

_)×7

a

2

b

7 =(-8)×

a

2 ×

b

×7×

a

2 ×

b

7 =(-8)×7×

a

2 ×

a

2 ×

b

×

b

7 =-56

a

4

b

8 (16)(-5

x

4

y

3_)×(-3

x

5

y

2₎ =(-5)×

x

4 ×

y

3 ×(-3)×

x

5 ×

y

2 =(-5)×(-3)×

x

4 ×

x

5 ×

y

3 ×

y

2 =15

x

9

y

5

L -`13 ( 1 )

ab

( 2 )-15

x

4

y

3 ( 3 )

a

9 ( 4 )-24

x

9

y

6 ( 5 )64

x

12

y

6 _{( 6 )}

b

10 ( 7 )20

x

10

y

5 _{( 8 )} -

a

11

b

14 ( 9 )49

b

9 ₍₁₀₎ -

a

6

b

7 (11)42

xy

(12)-15

x

5

y

17 (13)

x

11

y

(14)-

x

19 (15)-1

ab

(16)45

x

10

y

8 3 1 18 1 2 8 3 1 54 1 12 3 2 1 5 <풀이> ( 1 )

a

×

b

= × ×

a

×

b

( 1 )

a

×

b

=

ab

( 2 )3

x

4×(-5

y

3 )=3×(-5)×

x

4 ×

y

3=-15

x

4

y

3 ( 3 )(-2

a

8 )×&-

a

*=(-2)×&- *×

a

8 ×

a

( 3 )(-2

a

8 )×&-

a

*=

a

9 ( 4 )(-4

x

2

y

5_)×6

x

7

y

_=(-4)×6×

x

2 ×

x

7 ×

y

5 ×

y

=-24

x

9

y

6 ( 5 )_(-2

x

4₎3_×(-2

y

2₎3_=(-8

x

12_)×(-8

y

6₎ ( 5 )_(-2

x

4₎3_×(-2

y

2₎3_{=(-8)×(-8)×}

x

12×

y

6 ( 5 )(-2

x

4₎3_×(-2

y

2₎3 =64

x

12

y

6 3 2 3 4 3 4 1 5 2 5 1 2 2 5 1 2 (14)_(-2

xy

2₎3×3

x

2

y

=(-8

x

3

y

6 )×3

x

2

y

=(-8)×

x

3 ×

y

6 ×3×

x

2 ×

y

=(-8)×3×

x

3 ×

x

2×

y

6×

y

=-24

x

5

y

7 (15)₍

ab

₎2_×(2

a

2

b

₎3=

a

2

b

2 ×8

a

6

b

3 =

a

2 ×

b

2 ×8×

a

6 ×

b

3 =8×

a

2×

a

6×

b

2×

b

3 =8

a

8

b

5 (16)_(-2

xy

₎2_×(-3

xy

2₎2=4

x

2

y

2 ×9

x

2

y

4 =4×

x

2 ×

y

2 ×9×

x

2 ×

y

4 =4×9×

x

2×

x

2×

y

2×

y

4 =36

x

4

y

6 L - 12 ( 1 )9, 9, 9, 27 ( 2 )-32

x

2

y

3 ( 3 )25

a

8

b

2 _{( 4 )} -9

x

2

y

9 ( 5 )4, 4, 4, 12, 5 ( 6 )45

x

9 ( 7 )-16

b

11 _{( 8 )} -72

y

13 ( 9 )6, 6, 6, 7, 5 (10)-40

x

4

y

10 (11)16

a

7

b

5 ₍₁₂₎ -16

x

8

y

2 (13)2, 2, 2, 50, 5, 4 (14)-24

x

5

y

7 (15)8

a

8

b

5 ₍₁₆₎ 36

x

4

y

6 <풀이> ( 2 )4

x

2_×(-2

y

₎3 =4

x

2_×(-8

y

3₎ =4×

x

2_×(-8)×

y

3 =4×(-8)×

x

2 ×

y

3 =-32

x

2

y

3 ( 3 )(-

a

2 )4 ×(5

b

)2 =

a

8 ×25

b

2 =

a

8 ×25×

b

2 =25×

a

8 ×

b

2 =25

a

8

b

2 ( 4 )(-3

x

)2_×(-

y

3₎3 =9

x

2_×(-

y

9₎ =9×

x

2×(-1)×

y

9 =9×(-1)×

x

2 ×

y

9 =-9

x

2

y

9 ( 6 )5

x

×(3

x

4 )2 =5

x

×9

x

8 =5×

x

×9×

x

8 =5×9×

x

×

x

8 =45

x

9 ( 7 )(4

b

3₎2_×(-

b

₎5 =16

b

6_×(-

b

5₎ =16×

b

6 ×(-1)×

b

5 =16×(-1)×

b

6 ×

b

5 =-16

b

11 ( 8 )(-2

y

)3_×(-3

y

5₎2_=(-8

y

3_)×9

y

10 =(-8)×

y

3 ×9×

y

10 =(-8)×9×

y

3 ×

y

10 =-72

y

13 (10)5

x

4

y

×(-2

y

3 )3 =5

x

4

y

×(-8

y

9 ) =5×

x

4 ×

y

×(-8)×

y

9 =5×(-8)×

x

4 ×

y

×

y

9 =-40

x

4

y

10 (11)(-4

b

2₎2 ×

a

7

b

=16

b

4 ×

a

7

b

=16×

b

4×

a

7×

b

=16×

a

7 ×

b

4 ×

b

=16

a

7

b

5 (12)₍₂

x

2₎3_×(-2

x

2

y

2₎₌₈

x

6_×(-2

x

2

y

2₎ =8×

x

6_×(-2)×

x

2 ×

y

2 =8×(-2)×

x

6 ×

x

2 ×

y

2 =-16

x

8

y

2

13~14

L-1

정답및풀이

( 6 )_&-

b

4_* 2 ×

b

2 =

b

8 ×

b

2 ( 6 )_&-

b

4_*2×

b

2 = × ×

b

8 ×

b

2 ( 6 )_&-

b

4_*2×

b

2 =

b

10 ( 7 )5

x

2

y

5 ×(2

x

4 )2 =5

x

2

y

5 ×4

x

8 ( 7 )5

x

2

y

5_×(2

x

4₎2 =5×4×

x

2 ×

x

8 ×

y

5 ( 7 )5

x

2

y

5_×(2

x

4₎2 =20

x

10

y

5 ( 8 )_&

a

4

b

_* 2 ×&-

ab

4 * 3 =

a

8

b

2 ×&-

a

3

b

12 * = ×&- *×

a

8 ×

a

3×

b

2×

b

12 =-

a

11

b

14 ( 9 )(-7

b

5 )×(-7

b

4 )=(-7)×(-7)×

b

5 ×

b

4 ( 9 )_(-7

b

5_)×(-7

b

4₎=49

b

9 (10)_&-

a

2_* 3 ×9

b

7=&-

a

6 *×9

b

7 (10)_&-

a

2_*3×9

b

7 =&- *×9×

a

6 ×

b

7 (10)_&-

a

2_*3×9

b

7 =-

a

6

b

7 (11)6

x

×7

y

=6×7×

x

×

y

=42

xy

(12)_&-

x

5

y

3_*×(5

y

7)2 =&-

x

5

y

3 *×25

y

14 &-

x

5

y

3 *×(5

y

7 )2 =&- *×25×

x

5 ×

y

3 ×

y

14 &-

x

5

y

3 *×(5

y

7 )2 =-15

x

5

y

17 (13)

x

3

y

×

x

8 = × ×

x

3 ×

x

8 ×

y

(13)

x

3

y

×

x

8=

x

11

y

(14)_&-

x

5_* 2 ×&-

x

3 * 3 =

x

10 ×&-

x

9 * &-

x

5 *2 ×&-

x

3 * 3 = ×&- *×

x

10 ×

x

9 &-

x

5 *2 ×&-

x

3 * 3 =-

x

19 (15)6

a

×&-

b

*=6×&- *×

a

×

b

(15)6

a

×&-

b

*=-

ab

(16)_(-3

x

4

y

2₎2×5

x

2

y

4 =9

x

8

y

4 ×5

x

2

y

4 (16)(-3

x

4

y

2₎2 ×5

x

2

y

4 =9×5×

x

8 ×

x

2 ×

y

4 ×

y

4 (16)(-3

x

4

y

2 )2 ×5

x

2

y

4=45

x

10

y

8 1 3 1 18 1 18 1 18 1 8 4 9 1 8 4 9 1 2 2 3 1 2 2 5 5 4 2 5 5 4 3 5 3 5 3 5 8 3 8 27 8 27 2 3 1 54 8 27 1 16 8 27 1 16 2 3 1 4 1 12 3 4 1 9 3 4 1 9 3 4 1 3 L - 14 ( 1 )4, 4, 6 ( 2 )-7

x

6 ( 3 )-8

b

3 _{( 4 )} 2

y

5 ( 5 )5, 5, 5, 4 ( 6 ) -( 7 ) ( 8 ) ( 9 )

a

,

a

,

b

4 ₍₁₀₎ -7

xy

6 (11)-9

a

4 ₍₁₂₎ 5

x

2

y

3 (13)7, 7, - (14)

y

4 3 8

a

3

b

5 1 3

y

7 4

b

2

x

9 <풀이> ※ 단항식의 나눗셈은 분수 꼴로 고쳐 계산하거 나 나누는 단항식의 역수를 곱하는 두 가지 방법 으로 계산할 수 있고 그 결과는 같다. ( 1 )<다른 풀이> 24

a

5 ÷4

a

3 =24

a

5 × ( 1 )_{<다른 풀이> 24}

a

5÷4

a

3 =24× ×

a

5 × ( 1 )<다른 풀이> 24

a

5 ÷4

a

3 =6

a

2 ( 2 )42

x

9 ÷(-6

x

3 )= ( 2 )42

x

9×(-6

x

3 )= ( 2 )42

x

9_×(-6

x

3₎ =-7

x

6 ( 3 )_(-24

b

5_)÷3

b

2= ( 2 )(-24

b

5_)÷3

b

2 = ( 2 )_(-24

b

5_)÷3

b

2=-8

b

3 ( 4 )_(-14

y

6_)÷(-7

y

₎₌ ( 4 )(-14

y

6_)÷(-7

y

₎ = ( 4 )_(-14

y

6_)÷(-7

y

₎=2

y

5 ( 5 )_{<다른 풀이>} 40

a

5_÷(-8

a

9₎₌₄₀

a

5 × 40

a

5 ÷(-8

a

9 )=40×&- *×

a

5 × 40

a

5÷(-8

a

9 )=-

a

54 1

a

9 1 8 1 -8

a

9 (-14)×

y

6 (-7)×

y

-14

y

6 -7

y

(-24)×

b

5 3×

b

2 -24

b

5 3

b

2 42×

x

9 (-6)×

x

3 42

x

9 -6

x

3 1

a

3 1 4 1 4

a

3

( 6 )(-2

x

5_)÷18

x

4 = = =-( 7 )(-20

b

2_)÷(-5

b

4₎₌ ( 7 )(-20

b

2 )÷(-5

b

4 )= ( 7 )_(-20

b

2_)÷(-5

b

4₎= ( 8 )9

y

2 ÷27

y

9 = = = ( 9 )<다른 풀이> 54

ab

4 ÷6

a

=54

ab

4 × ( 9 )<다른 풀이> 54

ab

4 ÷6

a

=54× ×

ab

4 × ( 9 )<다른 풀이> 54

ab

4 ÷6

a

=9

b

4 (10)14

xy

8 ÷(-2

y

2 )= (10)14

xy

8 ÷(-2

y

2 )= (10)14

xy

8_÷(-2

y

2₎ =-7

xy

6 (11)(-36

a

6

b

3 )÷4

a

2

b

3 = (11)(-36

a

6

b

3_)÷4

a

2

b

3 = (11)(-36

a

6

b

3_)÷4

a

2

b

3 =-9

a

4 (12)(-15

x

7

y

6_)÷(-3

x

5

y

3₎₌ (12)(-15

x

7

y

6 )÷(-3

x

5

y

3 )= (12)(-15

x

7

y

6 )÷(-3

x

5

y

3 )=5

x

2

y

3 (13)_{<다른 풀이>} (-40

a

3

b

2 )÷5

b

7 =(-40

a

3

b

2 )× (-40

a

3

b

2 )÷5

b

7 =(-40)× ×

a

3

b

2 × (-40

a

3

b

2 )÷5

b

7 =-(14)6

x

4

y

4 ÷18

x

4 = (14)6

x

4

y

4÷18

x

4= (14)6

x

4

y

4 ÷18

x

4 = (15)_(-18

x

3

y

5_)÷(-9

x

4

y

8₎₌-18

x

3

y

5 -9

x

4

y

8

y

4 3 6×

x

4 ×

y

4 18×

x

4 6

x

4

y

4 18

x

4 8

a

3

b

5 1

b

7 1 5 1 5

b

7 (-15)×

x

7 ×

y

6 (-3)×

x

5 ×

y

3 -15

x

7

y

6 -3

x

5

y

3 (-36)×

a

6 ×

b

3 4×

a

2 ×

b

3 -36

a

6

b

3 4

a

2

b

3 14×

x

×

y

8 (-2)×

y

2 14

xy

8 -2

y

2 1

a

1 6 1 6

a

1 3

y

7 9×

y

2 27×

y

9 9

y

2 27

y

9 4

b

2 (-20)×

b

2 (-5)×

b

4 -20

b

2 -5

b

4

x

9 (-2)×

x

5 18×

x

4 -2

x

5 18

x

4 (15)(-18

x

3

y

5_)×(-9

x

4

y

8₎ = (15)(-18

x

3

y

5_)×(-9

x

4

y

8₎ = (16)8

x

8

y

3_÷(-32

x

4

y

8₎ (16)= 8

x

8

y

3 -32

x

4

y

8 2

xy

3 (-18)×

x

3 ×

y

5 (-9)×

x

4 ×

y

8 L - 15 ( 1 )4, 4, 4,

a

( 2 )-7

x

3 ( 3 )9

b

4 ( 4 )-25

y

3 ( 5 ) ( 6 ) -( 7 )- ( 8 ) ( 9 )4, 4, 4, 5 (10)-

x

7

y

6 (11)-4

ab

(12)9

x

2 (13) (14) -(15)- (16)8

x

2

y

2

ab

3 8 9

x

6

y

3 9

b

2

a

3 1 2

y

3 3

b

5

x

6 5 8

a

4 <풀이> ( 2 )56

x

9 ÷(-2

x

2 )3 =56

x

9 ÷(-8

x

6 ) ( 2 )56

x

9×(-2

x

2 )3 = ( 2 )56

x

9_×(-2

x

2₎3 = ( 2 )56

x

9 ×(-2

x

2 )3 =-7

x

3 ( 3 )(-6

b

5₎2_÷(2

b

3₎2 =36

b

10 ÷4

b

6 ( 3 )(-6

b

5₎2_÷(2

b

3₎2 = ( 3 )(-6

b

5 )2 ÷(2

b

3 )2 = ( 3 )(-6

b

5 )2 ÷(2

b

3 )2 =9

b

4 ( 4 )_(-5

y

4₎2_÷(-

y

₎5=25

y

8 ÷(-

y

5 ) ( 4 )_(-5

y

4₎2_÷(-

y

₎5= ( 4 )(-5

y

4₎2_÷(-

y

₎5 = ( 4 )(-5

y

4₎2_÷(-

y

₎5 =-25

y

3 25×

y

8 (-1)×

y

5 25

y

8 -

y

5 36×

b

10 4×

b

6 36

b

10 4

b

6 56×

x

9 (-8)×

x

6 56

x

9 -8

x

6

15~16

L-1

정답및풀이

( 5 )_(-4

a

₎2÷2

a

6 =16

a

2 ÷2

a

6 ( 3 )(-4

a

)2 ÷2

a

6 = ( 3 )_(-4

a

₎2÷2

a

6 = ( 3 )(-4

a

)2 ÷2

a

6 = ( 6 )_(-5

x

8_)÷(5

x

₎2_=(-5

x

8_)÷25

x

2 (6 )(-5

x

8_)÷(5

x

₎2 = ( 6 )(-5

x

8_)÷(5

x

₎2 = ( 6 )_(-5

x

8_)÷(5

x

₎2 =-( 7 )(-3

b

)3_÷(-3

b

4₎2_=(-27

b

3_)÷9

b

8 ( 7 )(-3

b

)3_÷(-3

b

4₎2 = ( 7 )(-3

b

)3 ÷(-3

b

4 )2 = ( 7 )_(-3

b

₎3_÷(-3

b

4₎2 =-( 8 )(2

y

3₎3_÷(2

y

3₎4 =8

y

9 ÷16

y

12 ( 8 )(2

y

3 )3 ÷(2

y

3 )4 = ( 8 )₍₂

y

3₎3_÷(2

y

3₎4= ( 8 )(2

y

3₎3_÷(2

y

3₎4 = (10)(-2

x

3

y

2 )3 ÷8

x

2 =(-8

x

9

y

6 )÷8

x

2 (10)_(-2

x

3

y

2₎3÷8

x

2 = (10)(-2

x

3

y

2₎3 ÷8

x

2 = (10)(-2

x

3

y

2 )3 ÷8

x

2 =-

x

7

y

6 (11)(6

ab

)2_÷(-9

ab

₎₌₃₆

a

2

b

2_÷(-9

ab

₎ (11)₍₆

ab

₎2_÷(-9

ab

₎= (11)(6

ab

)2_÷(-9

ab

₎ = (11)(6

ab

)2_÷(-9

ab

₎ =-4

ab

(12)(-3

x

4

y

₎2_÷(-

x

3

y

₎2 =9

x

8

y

2 ÷

x

6

y

2 (12)(-3

x

4

y

₎2_÷(-

x

3

y

₎2 = (12)_(-3

x

4

y

₎2_÷(-

x

3

y

₎2= (12)_(-3

x

4

y

₎2_÷(-

x

3

y

₎2=9

x

2 9×

x

8 ×

y

2

x

6 ×

y

2 9

x

8

y

2

x

6

y

2 36×

a

2 ×

b

2 (-9)×

a

×

b

36

a

2

b

2 -9

ab

(-8)×

x

9 ×

y

6 8×

x

2 -8

x

9

y

6 8

x

2 1 2

y

3 8×

y

9 16×

y

12 8

y

9 16

y

12 3

b

5 (-27)×

b

3 9×

b

8 -27

b

3 9

b

8

x

6 5 (-5)×

x

8 25×

x

2 -5

x

8 25

x

2 8

a

4 16×

a

2 2×

a

6 16

a

2 2

a

6 (13)_(-6

a

2

b

₎2÷4

a

7 =36

a

4

b

2 ÷4

a

7 (12)_(-6

a

2

b

₎2÷4

a

7 = (12)(-6

a

2

b

₎2 ÷4

a

7 = (12)_(-6

a

2

b

₎2÷4

a

7 = (14)₍₃

x

3₎2_÷(-

x

4

y

₎3=9

x

6 ÷(-

x

12

y

3 ) (14)₍₃

x

3₎2_÷(-

x

4

y

₎3= (14)(3

x

3₎2_÷(-

x

4

y

₎3 = (14)₍₃

x

3₎2_÷(-

x

4

y

₎3 =-(15)_(-2

a

3

b

7_)÷(-4

ab

2₎2_=(-2

a

3

b

7_)÷16

a

2

b

4 (15)(-2

a

3

b

7 )÷(-4

ab

2 )2 = (15)(-2

a

3

b

7_)÷(-4

ab

2₎2 = (15)_(-2

a

3

b

7_)÷(-4

ab

2₎2 =-(16)(2

x

2

y

2 )3 ÷(

x

2

y

4 )2 =8

x

6

y

6÷

x

4

y

8 (16)(2

x

2

y

2 )3 ÷(

x

2

y

4 )2 = (16)₍₂

x

2

y

2₎3_÷(

x

2

y

4₎2= (16)(2

x

2

y

2 )3 ÷(

x

2

y

4 )2 =8

x

2

y

2 8×

x

6 ×

y

6

x

4 ×

y

8 8

x

6

y

6

x

4

y

8

ab

3 8 (-2)×

a

3 ×

b

7 16×

a

2 ×

b

4 -2

a

3

b

7 16

a

2

b

4 9

x

6

y

3 9×

x

6 (-1)×

x

12 ×

y

3 9

x

6 -

x

12

y

3 9

b

2

a

3 36×

a

4 ×

b

2 4×

a

7 36

a

4

b

2 4

a

7 L - 16 ( 1 ) ,

a

2 , -6

a

2 _{( 2 )} -2

b

2 ( 3 ) ,

a

4 , ( 4 ) ( 5 )- ,

a

7

b

5 , - ( 6 ) ( 7 ) ( 8 )4,

a

2 , -48

a

4

b

( 9 )-

y

(10)-4

a

3 2 12

x

1 8

ab

2 4

x

4 9

y

5 2

b

2 3 2 9 5

a

3

b

4 12 12

b

4

a

3 6 5 3 4

<풀이> ※ 나누는 단항식에 분수가 포함되어 있으면 역 수를 곱하여 계산하는 방법을 이용한다. ( 2 )

b

9_÷&-

b

7_*=

b

9_{÷&- *} ( 3 )

b

9_÷&-

b

7_*=

b

9 ×&- * ( 3 )

b

9_÷&-

b

7_{*= ×&- *×}

b

9× ( 3 )

b

9_÷&-

b

7_*=-2

b

2 ( 4 )_&-

a

3

b

8_*÷&-

b

4_* =&-

a

3

b

8 *÷&- * =&-

a

3

b

8 *×&- * =&- *×&- *×

a

3

b

8 × = ( 6 )_&-

x

5

y

_*÷(-6

xy

6₎ =&-

x

5

y

*×&- * =&- *×&- *×

x

5

y

× = ( 7 )

a

2

b

÷

a

3

b

3=

a

2

b

÷ ( 9 )

a

2

b

÷

a

3

b

3 =

a

2

b

× ( 9 )

a

2

b

÷

a

3

b

3 = × ×

a

2

b

× ( 9 )

a

2

b

÷

a

3

b

3 = ( 9 )_&

xy

_* 2 ÷&-

x

3 * (11)=

x

2

y

2 ÷&- * (11)=

x

2

y

2 ×&- * (11)_{= ×&- *×}

x

2

y

2× (11)=-

y

2 12

x

1

x

3 3 4 1 9 3 4

x

3 1 9 4

x

3 3 1 9 4 3 1 3 1 8

ab

2 1

a

3

b

3 5 18 9 20 5 18

a

3

b

3 9 20 18

a

3

b

3 5 9 20 18 5 9 20 4

x

4 9

y

5 1

xy

6 1 6 8 3 1 6

xy

6 8 3 8 3 5

a

3

b

4 12 1

b

4 2 3 5 8 2 3

b

4 5 8 3

b

4 2 5 8 3 2 5 8 1

b

7 4 3 3 2 4 3

b

7 3 2 3

b

7 4 3 2 3 4 3 2 (10)(-

ab

2 )3 ÷&

b

3 * 2 =(-

a

3

b

6 )÷

b

6 (12)_(-

ab

2₎3_÷&

b

3_*2_=(-

a

3

b

6_)× (12)(-

ab

2₎3 ÷&

b

3 *2_=(-1)×4×

a

3

b

6 × (12)_(-

ab

2₎3_÷&

b

3_*2=-4

a

3 1

b

6 4

b

6 1 4 1 2 L - 17 ( 1 )-8

a

( 2 ) ( 3 )-4

b

5 ( 4 ) -( 5 )- ( 6 ) ( 7 )3

a

2

b

_{( 8 )} ( 9 )- (10) (11)- (12) (13)-10

y

3 ₍₁₄₎ 5

a

4

b

8 1 8

b

6

x

2

y

4 4 32

y

7

x

2 3

a

5 6 5

y

9

x

2

y

4 2 3

a

y

3 9

x

2 1 3

y

5 <풀이> ( 1 )(-56

a

7_)÷7

a

6 = ( 1 )_(-56

a

7_)÷7

a

7= ( 1 )_(-56

a

7_)÷7

a

7=-8

a

( 2 )_(-8

x

6_)÷(-24

x

6

y

5₎₌ ( 2 )(-8

x

6_)÷(-24

x

6

y

5₎ = ( 2 )_(-8

x

6_)÷(-24

x

6

y

5₎= ( 3 )₍₂

b

2₎3_÷(-2

b

₎₌₈

b

6_÷(-2

b

₎ ( 3 )(2

b

2 )3 ÷(-2

b

)= ( 3 )(2

b

2₎3_÷(-2

b

₎ = ( 3 )₍₂

b

2₎3_÷(-2

b

₎=-4

b

5 8×

b

6 (-2)×

b

8

b

6 -2

b

1 3

y

5 (-8)×

x

6 (-24)×

x

6 ×

y

5 -8

x

6 -24

x

6

y

5 (-56)×

a

7 7×

a

6 -56

a

7 7

a

6

17~18

L-1

정답및풀이

( 4 )_(-

x

2

y

3₎3_÷(-3

x

4

y

3₎2_=(-

x

6

y

9_)÷9

x

8

y

6 ( 4 )_(-

x

2

y

3₎3_÷(-3

x

4

y

3₎2= ( 4 )(-

x

2

y

3₎3_÷(-3

x

4

y

3₎2 = ( 4 )_(-

x

2

y

3₎3_÷(-3

x

4

y

3₎2

=-( 5 )_&-

b

3_*÷

ab

3_=&-

b

3_{*×& *}

( 5 )_&-

b

3_*÷

ab

3_{=&- *× ×}

b

3× ( 5 )_&-

b

3_*÷

ab

3 =-( 6 )(

x

2

y

₎2 ÷&

xy

3 * 2 =

x

4

y

2 ÷

x

2

y

6 ( 6 )(

x

2

y

₎2 ÷&

xy

3 *2 =

x

4

y

2 × ( 6 )(

x

2

y

)2 ÷&

xy

3 *2 =9×

x

4

y

2× ( 6 )₍

x

2

y

₎2_÷&

xy

3_*2= ( 7 )12

a

2

b

5_÷(-2

b

2₎2 =12

a

2

b

5 ÷4

b

4 ( 7 )12

a

2

b

5_÷(-2

b

2₎2 = ( 7 )12

a

2

b

5 ÷(-2

b

2 )2 = ( 6 )12

a

2

b

5_÷(-2

b

2₎2 =3

a

2

b

( 8 )_&-

y

5_*÷&-

y

6_*=&-

y

5_{*×&- *}

&-

y

5 *÷&-

y

6 *=&- *×&- *×

y

5 × &-

y

5 *÷&-

y

6 *= ( 9 )(-15

a

4_)÷5

a

9 = ( 7 )_(-15

a

4_)÷5

a

9= ( 7 )(-15

a

4_)÷5

a

9 =-(10)(2

x

2

y

5₎2 ÷&

x

2

y

* 3 =4

x

4

y

10 ÷

x

6

y

3 ( 9 )(2

x

2

y

5 )2 ÷&

x

3

y

*3 =4

x

4

y

10 × ( 9 )₍₂

x

2

y

5₎2_÷&

x

3

y

_*3=4×8×

x

4

y

10 × ( 9 )(2

x

2

y

5₎2 ÷&

x

3

y

*3 =32

y

7

x

2 1

x

6

y

3 8

x

6

y

3 1 8 1 2 3

a

5 (-15)×

a

4 5×

a

9 -15

a

4 5

a

9 6 5

y

1

y

6 3 2 4 5 3 2

y

6 4 5 2 3 4 5 12×

a

2 ×

b

5 4×

b

4 12

a

2

b

5 4

b

4 9

x

2

y

4 1

x

2

y

6 9

x

2

y

6 1 9 1 3 2 3

a

1

ab

3 8 9 3 4 8 9

ab

3 3 4 9 8 3 4

y

3 9

x

2 (-1)×

x

6 ×

y

9 9×

x

8 ×

y

6 -

x

6

y

9 9

x

8

y

6 (11)_&-

x

6

y

9_*÷

x

4

y

5 =&-

x

6

y

9 *× =&- *× ×

x

6

y

9 × =-(12)₍₂

b

2₎3_÷(4

b

4₎3=8

b

6 ÷64

b

12 (12)₍₂

b

2₎3_÷(4

b

4₎3= (12)(2

b

2₎3_÷(4

b

4₎3 = (12)(2

b

2₎3_÷(4

b

4₎3 = (13)(5

xy

2 )2 ÷&-

x

2

y

* =25

x

2

y

4 ÷&-

x

2

y

* =25

x

2

y

4 ×&- * =25×&- *×

x

2

y

4 × =-10

y

3 (14)_(-30

a

8

b

9_)÷(-6

a

4

b

₎₌ (14)(-30

a

8

b

9 )÷(-6

a

4

b

)= (14)(-30

a

8

b

9_)÷(-6

a

4

b

₎ =5

a

4

b

8 (-30)×

a

8 ×

b

9 (-6)×

a

4 ×

b

-30

a

8

b

9 -6

a

4

b

1

x

2

y

2 5 2 5

x

2

y

5 2 5 2 1 8

b

6 8×

b

6 64×

b

12 8

b

6 64

b

12

x

2

y

4 4 1

x

4

y

5 5 6 3 10 5 6

x

4

y

5 3 10 6 5 3 10 L - 18 ( 1 )36

a

5

b

2 _{( 2 )} -( 3 )-4

y

( 4 )

x

3

y

3 ( 5 ) ( 6 )-6

ab

2 ( 7 )- ( 8 ) ( 9 )-2

x

3 (10)-14

b

2

y

7 1

a

3

b

4

y

2 5

x

6

x

5

y

3

a

3

b

4 20

<풀이> ※

A

×

B

×

C

=

ABC

A

×

B

÷

C

=

A

×

B

× =

A

÷

B

×

C

=

A

× ×

C

=

A

÷

B

÷

C

=

A

× × = ( 1 )6

a

2

b

×3

a

3 ×2

b

( 2 )=6×3×2×

a

2

b

×

a

3 ×

b

( 2 )=36

a

5

b

2 ( 2 )<다른 풀이> 혼합 계산을 할 때에는 앞에서부터 순서대 로 계산해도 된다. 6

a

2

b

×3

a

3 ×2

b

=18

a

5

b

×2

b

=36

a

5

b

2 ( 2 )2

a

2×

ab

3×&-

b

* ( 2 )_{=2× ×&- *×}

a

2×

ab

3 ×

b

( 2 ) =-( 3 )3

xy

×(-8

y

)÷6

xy

=3

xy

×(-8

y

)× =3×(-8)× ×

xy

×

y

× =-4

y

<다른 풀이> 3

xy

×(-8

y

)÷6

xy

=(-24

xy

2 )÷6

xy

3

xy

×(-8

y

)÷6

xy

= 3

xy

×(-8

y

)÷6

xy

=-4

y

( 4 )3

x

3

y

2 ×

xy

4 ÷

xy

3 =3

x

3

y

2 ×

xy

4 × =3× × ×

x

3

y

2 ×

xy

4 × =

x

3

y

3 ( 5 )(-9

x

2

y

)÷3

xy

3 ×(-2

x

4

y

) =-9

x

2

y

× ×(-2

x

4

y

₎ =(-9)× ×(-2)×

x

2

y

× ×

x

4

y

=6

x

5

y

1

xy

3 1 3 1 3

xy

3 1

xy

3 5 6 2 5 5 6

xy

3 2 5 6 5 2 5 -24

xy

2 6

xy

1

xy

1 6 1 6

xy

3

a

3

b

4 20 1 10 3 4 1 10 3 4

A

BC

1

C

1

B

AC

B

1

B

AB

C

1

C

<다른 풀이> (-9

x

2

y

)÷3

xy

3 ×(-2

x

4

y

) = ×(-2

x

4

y

) = ×(-2

x

4

y

₎ = ( 6 )(-2

ab

)3 ÷4

a

4

b

2×3

a

2

b

=(-8

a

3

b

3 )÷4

a

4

b

2 ×3

a

2

b

=(-8

a

3

b

3 )× ×3

a

2

b

=(-8)× ×3×

a

3

b

3 × ×

a

2

b

=-6

ab

2 ( 7 )3

x

2

y

÷(-10

x

3

y

)×

y

2 =3

x

2

y

×&- *×

y

2 =3×&- *× ×

x

2

y

× ×

y

2 =-( 8 )6

a

3

b

÷2

a

2

b

3÷3

a

4

b

2 =6

a

3

b

× × =6× × ×

a

3

b

× × = <다른 풀이> 6

a

3

b

÷2

a

2

b

3 ÷3

a

4

b

2 = ÷3

a

4

b

2 = × = ( 9 )50

x

5

y

2÷(5

xy

3 )2 ÷(-

y

)3 =50

x

5

y

2 ÷25

x

2

y

6 ÷(-

y

3 ) =50

x

5

y

2 × ×&- * =50× ×(-1)×

x

5

y

2 × × =-2

x

3

y

7 1

y

3 1

x

2

y

6 1 25 1

y

3 1 25

x

2

y

6 1

a

3

b

4 1 3

a

4

b

2 3

a

b

2 6

a

3

b

2

a

2

b

3 1

a

3

b

4 1

a

4

b

2 1

a

2

b

3 1 3 1 2 1 3

a

4

b

2 1 2

a

2

b

3

y

2 5

x

1

x

3

y

2 3 1 10 2 3 1 10

x

3

y

2 3 1

a

4

b

2 1 4 1 4

a

4

b

2 6

x

5

y

-3

x

y

2 -9

x

2

y

3

xy

3

18~19

L-1

정답및풀이

L - 19 ( 1 )-30

x

3

y

6 _{( 2 )} ( 3 )2

a

3

b

6 _{( 4 )} -16 ( 5 )-8

a

9

b

7 _{( 6 )} -2

a

6

b

( 7 ) ( 8 )1 ( 9 )-2

x

(10)3

x

y

5

y

5

a

4

b

2 4

a

50 <풀이> ( 1 )3

xy

2×(-5

y

3 )×2

x

2

y

=3×(-5)×2×

xy

2 ×

y

3 ×

x

2

y

=-30

x

3

y

6 ( 2 )

a

2

b

×

ab

2 ÷10

a

2

b

3 =

a

2

b

×

ab

2 × = × ×

a

2

b

×

ab

2 × = ( 3 )(-5

a

2

b

_)÷(-10

ab

_)×(-2

ab

3₎2 =(-5

a

2

b

)÷(-10

ab

)×4

a

2

b

6 =(-5

a

2

b

)×&- *×4

a

2

b

6 =(-5)×&- *×4×

a

2

b

× ×

a

2

b

6 =2

a

3

b

6 ( 4 )12

x

2

y

÷&-

y

*÷(-

x

)2 =12

x

2

y

÷&-

y

*÷

x

2 =12

x

2

y

×&- *× =12×&- *×

x

2

y

× × =-16 1

x

2 1

y

4 3 1

x

2 4 3

y

3 4 3 4 1

ab

1 10 1 10

ab

a

50 1

a

2

b

3 1 10 1 5 1 10

a

2

b

3 1 5 1 5 (10)(-12

a

2

b

6 )÷(-2

a

)÷&-

ab

4 * =(-12

a

2

b

6 )×&- *×&- * =(-12)×&- *×&- *×

a

2

b

6 × × =-14

b

2 1

ab

4 1

a

7 3 1 2 7 3

ab

4 1 2

a

3 7 ( 5 )_(-

a

2

b

₎3×2

a

3

b

2 ×(-2

b

)2 =(-

a

6

b

3_)×2

a

3

b

2 ×4

b

2 =(-1)×2×4×

a

6

b

3 ×

a

3

b

2×

b

2 =-8

a

9

b

7 ( 6 )6

a

9

b

2 ÷(-3

a

3 )÷

b

=6

a

9

b

2 ×&- *× =6×&- *×

a

9

b

2 × × =-2

a

6

b

( 7 )3

a

2

b

4 ÷&-

b

2 *×&-

a

2 * =3

a

2

b

4 ×&- *×&-

a

2 * =3×&- *×&- *×

a

2

b

4 × ×

a

2 = ( 8 )8

x

2

y

÷

x

4

y

3 ×&-

xy

* 2 =8

x

2

y

÷

x

4

y

3 ×

x

2

y

2 =8

x

2

y

× ×

x

2

y

2 =8× × ×

x

2

y

× ×

x

2

y

2 =1 ( 9 )(-3

xy

2₎2 ×

x

2_÷(-15

x

3

y

5₎ =9

x

2

y

4×

x

2÷(-15

x

3

y

5 ) =9

x

2

y

4 ×

x

2 ×&- * =9× ×&- *×

x

2

y

4 ×

x

2 × =-(10)

x

3

y

2×(2

xy

3₎2 ÷

x

6

y

7 =

x

3

y

2×4

x

2

y

6÷

x

6

y

7 =

x

3

y

2 ×4

x

2

y

6 × = ×4× ×

x

3

y

2 ×

x

2

y

6 × =3

_x

y

1

x

6

y

7 3 2 1 2 3 2

x

6

y

7 1 2 2 3 1 2 2 3 1 2 2

x

5

y

1

x

3

y

5 1 15 2 3 1 15

x

3

y

5 2 3 2 3 2 3 1

x

4

y

3 9 16 2 9 9 16 2 9

x

4

y

3 9 16 9 2 3 4 9 2 5

a

4

b

2 4 1

b

2 1 4 5 3 1 4 5 3

b

2 1 4 3 5 1

b

1

a

3 1 3 1

b

1 3

a

3

L - 20 ( 1 )-6

ab

( 2 ) ( 3 )15

x

4

y

2 _{( 4 )} -

a

3

b

6 ( 5 )-10

x

( 6 ) -( 7 )- ( 8 )4

a

8

b

( 9 ) 1 (10)18

a

4

b

6

x

2

y

3

y

3 2

x

3 5

a

5

b

6 4

y

4 2 <풀이> ( 1 )(-16

a

2

b

)×3

b

÷8

ab

=(-16

a

2

b

)×3

b

× =(-16)×3× ×

a

2

b

×

b

× =-6

ab

( 2 )18

x

2

y

5_÷(-2

x

₎2 ÷9

y

=18

x

2

y

5 ÷4

x

2 ÷9

y

=18

x

2

y

5 × × =18× × ×

x

2

y

5 × × = <다른 풀이> 18

x

2

y

5÷(-2

x

)2 ÷9

y

=18

x

2

y

5÷4

x

2 ÷9

y

18

x

2

y

5_÷(-2

x

₎2 ÷9

y

= × 18

x

2

y

5 ÷(-2

x

)2 ÷9

y

= ( 3 )9

x

2

y

×5

x

×

xy

=9×5× ×

x

2

y

×

x

×

xy

=15

x

4

y

2 ( 4 )_(-

a

2

b

3₎2_÷&-

ab

_* 2 ×&-

ab

2 * =

a

4

b

6 ÷

a

2

b

2 ×&-

ab

2 * =

a

4

b

6 × ×&-

ab

2 * =4×&- *×

a

4

b

6 × ×

ab

2 =-

a

3

b

6 1

a

2

b

2 1 4 1 4 4

a

2

b

2 1 4 1 4 1 4 1 2 1 3 1 3

y

4 2 1 9

y

9

y

5 2

y

4 2 1

y

1

x

2 1 9 1 4 1 9

y

1 4

x

2 1

ab

1 8 1 8

ab

( 5 )5

x

2

y

÷(-3

xy

2 )×6

y

=5

x

2

y

×&- *×6

y

=5×&- *×6×

x

2

y

× ×

y

=-10

x

( 6 )_&

ab

_* 2 ×(-5

a

3_)×(-

b

₎4 =

a

2

b

2_×(-5

a

3_)×

b

4 = ×(-5)×

a

2

b

2 ×

a

3 ×

b

4 =-( 7 )(2

xy

2₎2 ×

xy

2_÷(-

x

2

y

₎3 =4

x

2

y

4 ×

xy

2_÷(-

x

6

y

3₎ =4

x

2

y

4×

xy

2×&- * =4× ×(-1)×

x

2

y

4 ×

xy

2 × =-( 8 )(-2

ab

)3 ×3

a

5÷(-6

b

2 ) =(-8

a

3

b

3 )×3

a

5 ÷(-6

b

2 ) =(-8

a

3

b

3 )×3

a

5 ×&- * =(-8)×3×&- *×

a

3

b

3 ×

a

5 × =4

a

8

b

( 9 )_(-4

x

2

y

3_)÷

x

3

y

2_÷(-12

xy

4₎ =(-4

x

2

y

3_)× ×&- * =(-4)×3×&- *×

x

2

y

3 × × = (10)8

a

4

b

÷& * 2 ×(

a

2

b

)3 =8

a

4

b

÷ ×

a

6

b

3 =8

a

4

b

× ×

a

6

b

3 =8× ×

a

4

b

× ×

a

6

b

3 =18

a

4

b

6

b

2

a

6 9 4 9

b

2 4

a

6 4

a

6 9

b

2 2

a

3 3

b

1

x

2

y

3 1

xy

4 1

x

3

y

2 1 12 1 12

xy

4 3

x

3

y

2 1 3 1

b

2 1 6 1 6

b

2

y

3 2

x

3 1

x

6

y

3 1 8 1

x

6

y

3 1 8 1 8 1 8 5

a

5

b

6 4 1 4 1 4 1 2 1

xy

2 1 3 1 3

xy

2

21~22

L-1

정답및풀이

L - 21 ( 1 )28

x

3

y

2 ( 2 )-27

a

13

b

13 ( 3 )- ( 4 )7

a

2

b

3 ( 5 ) ( 6 ) -( 7 ) ( 8 )-2

x

3

y

2 ( 9 )2

ab

(10) -(11)2

b

(12)2

y

6

a

2

x

12 2

a

4

b

7 9 6

a

2 1 8

x

4

y

3

x

2

y

3 <풀이> ( 2 )(

a

2

b

5₎2_×(-3

a

3

b

₎3 =

a

4

b

10_×(-27

a

9

b

3₎ ( 2 )(

a

2

b

5₎2_×(-3

a

3

b

₎3 =-27

a

13

b

13 ( 4 )(-63

a

7

b

6_)÷(-9

a

5

b

3₎₌ ( 4 )_{( - 6 3}

a

7

b

6_{) ÷ (} -9

a

5

b

3₎ =7

a

2

b

3 ( 5 )2

x

2

y

_÷(4

x

3

y

2₎2 =2

x

2

y

÷16

x

6

y

4 ( 5 )2

x

2

y

_÷(4

x

3

y

2₎2 = ( 5 )2

x

2

y

_÷(4

x

3

y

2₎2 = ( 6 )

a

3_÷&-

a

5_*=

a

3_×&- *=-( 7 )6

ab

×&-

a

* 3 ×(-

b

2 )3 =6

ab

×&-

a

3 *×(-

b

6 ) = ( 8 )(-4

xy

2 )×3

x

3

y

÷6

xy

=(-4

xy

2_)×3

x

3

y

× =-2

x

3

y

2 ( 9 )

b

2×12

a

2

b

÷

ab

2 =

b

2 ×12

a

2

b

× ( 9 )

b

2×12

a

2

b

÷

ab

2 =2

ab

(10)

xy

2_÷(-2

xy

₎3×

x

3

y

=

xy

2_÷(-8

x

3

y

3_)×

x

3

y

=

xy

2 ×&- 1 *×

x

3

y

8

x

3

y

3 2 3 2 3 2 3 4 3

ab

2 1 8 3 4 1 8 1 6

xy

2

a

4

b

7 9 1 27 1 3 6

a

2 4 3

a

5 9 2 3 4 9 2 1 8

x

4

y

3 2

x

2

y

16

x

6

y

4 -63

a

7

b

6 -9

a

5

b

3 (11)(-3

a

2

b

3 )÷&- * 2 ×(-6

a

2

b

₎ =(-3

a

2

b

3 )÷ ×(-6

a

2

b

) =(-3

a

2

b

3_{)× ×(-6}

a

2

b

₎ = (12)_(-6

xy

₎2÷9

x

2 ÷2

y

(12)=36

x

2

y

2 ÷9

x

2 ÷2

y

(12)=36

x

2

y

2 × × (12)=2

y

1 2

y

1 9

x

2 2

b

6

a

2

b

2 9

a

6 9

a

6

b

2 3

a

3

b

L - 22 ( 1 )- ( 2 )12

x

5

y

3 ( 3 )3

a

2

b

_{( 4 )} ( 5 )- ( 6 )-2

x

4

y

5 ( 7 )36

x

2

y

6 ( 8 ) -( 9 ) (10)-8

b

2 (11) (12)-4

a

12

b

5

x

6

y

4 4

y

11

z

3 27

x

2 12

b

3

a

2

a

4

xy

5 8

a

2

b

8 <풀이> ( 1 )(-2

a

2₎3_÷(

a

2

b

4₎2_=(-8

a

6_)÷

a

4

b

8 ( 1 )_(-2

a

2₎3_÷(

a

2

b

4₎2= ( 1 )(-2

a

2 )3 ÷(

a

2

b

4 )2 =-( 2 )3

x

2 ×4

xy

×(-

xy

)2 =3

x

2 ×4

xy

×

x

2

y

2 ( 2 )3

x

2 ×4

xy

×(-

xy

)2 =12

x

5

y

3 ( 4 )4

x

2

y

2 ÷10

x

4

y

×

x

3 ( 4 )=4

x

2

y

2 × ×

x

3 ( 4 )=

xy

5 1 2 1 10

x

4

y

1 2 8

a

2

b

8 -8

a

6

a

4

b

8

( 5 )_&-

a

2

b

_* 2 ÷(-

a

3

b

2 ) ( 5 )=

a

4

b

2÷(-

a

3

b

2 ) ( 5 )=

a

4

b

2×&- * ( 5 ) =-( 6 )8

x

4

y

3 ×(-

xy

)2 ÷(-4

x

2 ) =8

x

4

y

3 ×

x

2

y

2_÷(-4

x

2₎ =8

x

4

y

3 ×

x

2

y

2 ×&- * =-2

x

4

y

5 ( 7 )_(-3

xy

₎2×4

y

4 =9

x

2

y

2 ×4

y

4 =36

x

2

y

6 ( 8 )2

a

3

b

4 ÷&-

a

2

b

* 3 ÷ =2

a

3

b

4 ÷&-

a

6

b

3 *÷ =2

a

3

b

4 ×&- *× =-( 9 )(

xy

2 )4 ÷& * 3 =

x

4

y

8 ÷ ( 9 )(

xy

2₎2 ÷& *3 =

x

4

y

8 × ( 9 )₍

xy

2₎2_{÷& *}3= (10)4

a

3

b

4÷3

a

3

b

4×(-6

b

2 ) =4

a

3

b

4 × ×(-6

b

2₎ =-8

b

2 (11)_&-

x

2

y

_* 2 ×&-

xy

* 2 (11)=

x

4

y

2 ×

x

2

y

2 (11)= (12)(-

a

2

b

)4 ×&- *÷& * 2 =

a

8

b

4 ×&- *÷ =

a

8

b

4×&- *× =-4

a

12

b

5 4

a

6

b

4

b

5

a

2

b

4 4

a

6

b

5

a

2

b

2 2

a

3

b

5

a

2

x

6

y

4 4 1 9 9 4 1 3 3 2 1 3

a

3

b

4

y

11

z

3 27

x

2

y

3

z

3 27

x

6 27

x

6

y

3

z

3 3

x

2

yz

12

b

3

a

2 3

ab

2 4 8

a

6

b

3 4 3

ab

2 1 8 4 3

ab

2 1 2 1 4

x

2

a

4 1

a

3

b

2 1 4 1 4 1 2 L - 23 ( 1 )14

b

2+4

b

-18 ( 2 )-8

x

2+2

x

-4 ( 3 )2

y

2 -5

y

+6 ( 4 )14

a

2 -

a

( 5 )2

b

2 -4

b

+2 ( 6 )6

x

2 +2

x

+10 ( 7 )-8

y

2 -5

y

-34 ( 8 )3

b

2 -7

b

-7 ( 9 )

x

2+8

x

+1 (10)-2

y

2-11

y

-2 (11)4

a

2 +9

a

(12)-6

b

2 +5

b

+10 (13)9

x

2 -17

x

-13 (14)-

y

2 -3

y

+2 <풀이> ※ 이차식의 덧셈, 뺄셈도 일차식의 덧셈, 뺄셈과 같은 방법으로 이차항은 이차항끼리, 일차항은 일 차항끼리, 상수항은상수항끼리간단히한다. �괄호를풀때 괄호앞이+이면�괄호안의부호는그대로 괄호앞이-이면�괄호 안의 각 항의 부호를 반대로 ( 1 )2(4

b

2 +3

b

-5)+(6

b

2 -2

b

-8) =8

b

2 +6

b

-10+6

b

2 -2

b

-8 =8

b

2 +6

b

2 +6

b

-2

b

-10-8 =14

b

2 +4

b

-18 ( 2 )(

x

2 +2

x

-7)+3(-3

x

2 +1) =

x

2 +2

x

-7-9

x

2 +3 =

x

2 -9

x

2 +2

x

-7+3 =-8

x

2 +2

x

-4 ( 3 )(-6

y

2 -

y

+2)+4(2

y

2 -

y

+1) =-6

y

2 -

y

+2+8

y

2 -4

y

+4 =-6

y

2 +8

y

2 -

y

-4

y

+2+4 =2

y

2 -5

y

+6 ( 4 )2(

a

2 -2

a

)+3(4

a

2 +

a

) =2

a

2 -4

a

+12

a

2 +3

a

=2

a

2 +12

a

2 -4

a

+3

a

=14

a

2 -

a

( 5 )2(-4

b

2 -

b

)+2(5

b

2 -

b

+1) =-8

b

2 -2

b

+10

b

2 -2

b

+2 =-8

b

2 +10

b

2 -2

b

-2

b

+2 =2

b

2 -4

b

+2 ( 6 )4(

x

2 -

x

+3)+2(

x

2 +3

x

-1) =4

x

2 -4

x

+12+2

x

2 +6

x

-2 =4

x

2 +2

x

2 -4

x

+6

x

+12-2 =6

x

2 +2

x

+10 ( 7 )-3(4

y

2 -3

y

+8)+2(2

y

2 -7

y

-5) =-12

y

2 +9

y

-24+4

y

2 -14

y

-10 =-12

y

2 +4

y

2 +9

y

-14

y

-24-10 =-8

y

2 -5

y

-34 ( 8 )4(

b

2 -

b

-2)-(

b

2 +3

b

-1) =4

b

2 -4

b

-8-

b

2 -3

b

+1 =4

b

2 -

b

2 -4

b

-3

b

-8+1 =3

b

2 -7

b

-7