Download Exponent Rules

Rules of Exponents
Product Rule
If m and n are positive integers and a is a real number, then a m a n
x 2 x5
x2
5
x7
x8 x x 3
x8
1 3
x12
am n .
b5 b 2 b 3 b b 5
2 3 1
b11
Power Rule
If m and n are positive integers and a is a real number, then (a m )n
( s 2 )3
s2 3
s6
(t 2 ) 4
t2 4
t8
(u 7 ) 4
a mn .
u7 4
u 28
Power of a Product
If n is a positive integer and a and b are real numbers, then (ab) n
(2c)3
23 c3
8c3
(3xy 2 z 4 )3
33 x3 y 6 z12
a nb n .
27 x3 y 6 z12
Power of a Quotient
If n is a positive integer and a and c are real numbers,
n
a
then
c
m
n
7
an
provided c
cn
x3
3 y5
m7
n7
0
4
x12
34 y 20
x12
81y 20
2abc8
3a 3bc3
2
22 a 2b 2c16
32 a 6b 2 c 6
Quotient Rule
If m and n are positive integers and a is a real number, then
x5
x2
x5
2
2 x5 y 2
xy
x3
2 x5 1 y 2
1
2 x4 y
am
an
4 x5 y 7
2 x4 y3
2 xy 4
Zero Exponents
a0
1, as long as a
30 1
(ab)0
0
1
( 5)0
1
50
am n .
1
4a 2b 2c16
9a 6 b 2 c 6