1. กก
ก ก F F
กF ก F F
F

2. กก
กก
F a n ก
an = a ⋅a ⋅ . . .⋅a
n
ก a F กก
ก n F ก
3
F 2 = 2⋅2⋅2 = 8

3. F a,b m,n
1. a m a n = a m +n F 2 2 ⋅ 2 4 = 2 2+ 4 = 26
2. (a m ) n = a mn F (52 ) 6 = 52⋅6 = 512
3. (ab ) m = a m b m F ( 2 ⋅ 3) 2 = 2 2 ⋅ 3 2 = 36
m 2
4. a  am F 3 32 9
  = , b ≠0   = 2 =
b  bm 4 4 16

4. F n กa
a ≠ 0 F a −n
=
1
an
F
1 1
−2
= = a2 , a ≠ 0
a 1
a2

5. F a a ≠0 F a0 = 1
am
= a m −n
an
F 28
= a 8−3 = a 5
23
3−1 6
= = 2
6 −1 3

6. กก nn
กF F x ก aก F x2 = a
x a F ก
ก 1 a ก
ก a ก F a
ก a F − a

7. ก 2 F a F
ก a 0
ก 3 F a
ก a F F
>> a a ≥ 0 F

8. a2 = |a|
ก F กF ก ก F
F −
1 ก 1 F 1
(− )2 =
1
2 4 2 4
3 ก 3 F ( 3) 2 = 3
-4 ก 16 F ( −4 ) 2 = 16
4 = 22 = | 2| = 2
( −2 ) 2 = | − 2| = − 2

9. กก
Fx>0 y>0
1. x y = xy
2. x
=
x
y y
F 1. 2 3 = 2×3 = 6
2. 2
3
=
2
3
3. 2
=
2 3
=
2×3
=
6
3 3 3 3×3 3

10. กก
กก กก กก
F x ก n ก
กก F 1 F
1
xn = n x
F 1
2 16
16 2 = = 16 = 4
1
 1 4 4 1 1
  = =
 81  81 2

11. F x กm n
n>m
0 F  1 
 
m
x n =  xn 
 
 
F 2
2  1 
 
64 3 =  64 3 
 
 
3
3  1
3
 1 4  1  4  1  1
  =    =   =
 81   81   3 27
 

12. กก กก FF กก FF
F F 3 2 + 50 + 32
3 2 + 50 + 32 = 3 2 + 25 × 2 + 16 × 2
= 3 2 + 52 × 2 + 42 × 2
= 3 2 +5 2 + 4 2
= 12 2

13. F 3 + 2
F F F F ก F
3 − 2
3 + 2
= 3 + 2
×
3 + 2
3 − 2 3 − 2 3 + 2
= 3 + 3 2 + 3 2 +2
3 −2
= 3 +2 3 2
= 3 +2 6

14. F F 2 8 × 125 × 40
= 2 2 2 ( 2) × 5 2 (5) × 4 2 (10 )
= 4 2 × 5 5 × 2 10
= 40 × 2 × 5 × 10
= 40 × 10
= 400

15. x2 −y2 + x
F F x2 + y2 −y
x2 + y2 + y x − x 2 −y 2
x2 −y2 + x x2 + y2 −y
2 2
÷
x + y + y x − x 2 −y 2
= x2 −y2 + x
×
x − x2 −y2
2 2
x + y + y x 2 +y 2 − y
= x + x2 −y2
× x − x2 −y2
2 2
x + y + y x 2 +y 2 − y
x 2 − (x 2 − y 2 ) y2
= =
x 2 +y 2 −y 2 x2

16. ก