Power of a Product Property of Exponents

To find a power of a product, find the power of each factor and then multiply.  In general, ( ab ) m = a m b m .

Example 1:

Simplify ( 3t ) 4

( 3t ) 4 = 3 4 t 4 =81 t 4

Suppose you want to multiply two powers with the same exponent but different bases.  By using the commutative property of multiplication, you can rewrite the rule as

          a m b m = ( ab ) m .

Example 2:

Simplify 3 2 4 2

3 2 4 2 =( 33 )( 44 ) =( 34 )( 34 ) = 12 2

In other words, you can keep the exponent the same and multiply the bases.