Summary of Exponent Rules with examples
NOTE: rules of exponents only apply to multiplication and division problems
a
b
ab
1. x  x  x
(when multiplying like bases, add exponents) NOTE: keep the same base!
x 4 x7
x11 ,
35 34
a b
a b
2. ( x )  x
6
x5
x 30 ,
39,
( 2)
4
( 2)7
( 2)3,
x 2/3 x 5/3
x 7/3
(when raising a base to a power and then raising to a power again, multiply the exponents)
2
43
46
51/2
256,
7
57/2,
2/5
x1/3
x 2/15
a
3. ( xy)
a
a a
x y
x
xa
(when raising a product or quotient to a power, raise
4.   
a
y
 
y
and
each factor to that power)
3 xy
2 3
xa
5.
x
33 x 3 ( y 2 )3
7
x
x4
30
7. x
27 x 3 y 6 ,
1/3
27 x 2
1/3
3 x 2/3
y 1/6
1/3
y 1/2
 x a  b (when dividing like bases, subtract the exponents)
b
6. x
27 x 2
y 1/2
x7
0
4
( 8)2
a

1
xa
1
x
and
1(a, b
x (4/5)
1
x a
 5x 7 
3
3x6
7y
7
4

251/2
2,
81/3
5,
16
4,
00
3
8
( 32)1/5
( 64)3/4 is not real , ( 64)5/3
25
( 1/2)
( 36)1/2 is not real,
5
3
27( 1/3)
3x 6 y4
7
a power

x b root
25
x (12/15)
(5/15)
x 7/15
undefined
 x a (a negative exponent on a “factor” moves that factor to the “other” part of the fraction)
5
x
(1/3)
0)
8. x1/ b  b x and xa / b  b (xa )
161/2
x 4/5
x1/3
64,
 1 (anything raised to the 0 power, except 0, is equal to 1)
1, (a2b3 )0
x 3 
( 8)9
( 8)7
x 3,
32
5
64
5,
( 4)5
493/2

251/2
1/3
27
5
3
( 27)1/3
( 49)3
1024,

9
3/2
73
1
93/2
3
27
343,
1
27
3,