SIMPLIFYING EXPONENTS
ZERO POWER RULE:
a0  1
(any term to the zero power is one)
Examples
1. (m5n7 )0 
2. (4m8n2 )(2mn4 )0 
PRODUCT RULE:
a m a n  a m n
(when multiplying LIKE bases, add the powers)
Examples:
1. x 4 x5 
2. 55 58 
3. a7 a a12 
4. (3x6 )(2 x4 ) 
5. (4m8n2 )(2mn4 )(5m4 n3 ) 
QUOTIENT RULE:
am
 a mn
n
a
(when dividing with LIKE bases, subtract the powers)
Note: it is always the numerator's power minus the denominator's power
Examples:
1.
x6

x4
2.
m5 n 7

m4 n10
3.
a 3b7

a 5b9
NEGATIVE POWER RULE:
an 
1
an
(this is simply a variation of the quotient rule)
Examples:
1. 3x 4 
2.
5m 8 n 2
x10 y 5
POWER RULE:
(a mbn )k  a mk bnk
(when taking a monomial to a power, distribute the power to each
element of the monomial including the coefficient)
Examples:
1. (a 4b3 )2 
3. (2 xy 7 z 2 )5 
2. (3m2 n5 )4 
4.
(6a 9b6 ) 2

( c 4 d 2 ) 5
REMEMBER: The power rule does NOT work when elements are being added within the parenthesis!
(a m  bn )k  a mk  bnk