1. x ax
ax
x y x=y ax
ax = a y
x ,y
n
a a
1
n
n
a n 1
a n

2. 1
an n
a
a p,q (p,q)
1
= 1 , q>0 a q
R
p<0 a 0
p 1
a q
(a ) p
q
1 a q p
ap
ap q
2 m,n a
am an

3. am an am n
3 m,n a
am an
(am)n = amn
4 n a ,b
an bn
(ab)n = anbn
5 n a ,b
an bn
a an
b 0 ( )n
b bn
6 m, n a
0 am an

4. am
am n
an
1
3 6
(27a )
1 1 1
3 6
(27a ) = (27) 6 (a 3 ) 6
1 1
= 3 6 3 6
(3 ) (a )
1 1
= 32 a2
1
= (3a ) 2
1
(8xy 2 ) 3 x>0 , y>
1
(16x 2 y 2 4
)
0
1 1 1 2
2 3
= 83
(8xy ) x 3y 3
1 1 1 1
(16x 2 y 2 ) 4 16 4 x 2 y 2
1
3 3 1 1 2 1
(2 ) ( ) ( )
= 1
x 3 2 y 3 2
4 4
(2 )
1 1
= (x 6 )( y 6 )
1
y 6
= 1
x 6
1
y
= ( )6
x

5. 2a 2 y 4 4
( )
5z 3
2a 2 y 4
(2a 2 y 4 ) 4
(
3
) 4
=
5z (5z 3 ) 4
= 2 4 a 8 y 16
5 4 z 12
= 5 4 y 16
= 625 y 14
2 4 a 8 z 12 16 a 8 z 12
7n 2
35 7 n 1
7 n 11
=
2 1
7n 35 7 n 7n 72 5 7 7n 1
7n 11 7 n 11
= 7n 72 5 7n
7 n 11
= 7 n (7 2 5)
7 n 11
= 49 5
11
= 4

6. 1. x>0 , x 0 ,m n
............ 2.1 1 1
xm n
……….2.2 xm
xm n
xm xn xn
……….2.3 1
xn ……….2.4 xm xn xm n
xn
……….2.5 xm
x0 xn xm
xn
……….2.6 xm
xp m–n–p = 0
xn

7. 1. = ………………………………………………. a R
2. a = …………………………………………………. a R
3. = …………………………………………….…. x R
4. = ………………………………………….…. y R
y≠0
5. =……………………………………………...
m R m≠0
6. =…………………………………………………...
m R
7. =…………………..………………………………... b R
8. =…………………..………………………………...
R
9. = ………………………………………….…. x,y R
y≠0

8. 10. =………………………………………….…. p,q R
q≠0
1. =…………………………………………………………..
2. =…………………………………………………………..
3. =…………………………………………………………..
4.
=…………………………………………………………..
5. =…………………………………………………………..
6. =…………………………………………………………..
7. =…………………………………………………………..
8. =…………………………………………………………..

9. 9. =………………………………………………………
…..
10.
=…………………………………………………………..
11.
=…………………………………………………………..
12.
=…………………………………………………………..
1.
=………………………………………………………………
…………………………
………………………………………………………………
…………………………..
2.

10. =………………………………………………………………
…………………………
………………………………………………………………
…………………………..
3.
=………………………………………………………………
…………………………
………………………………………………………………
…………………………..
4.
=………………………………………………………………
…………………………
………………………………………………………………
…………………………..
5.
=………………………………………………………………
…………………………
………………………………………………………………
…………………………..