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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 =( 3⋅3 )⋅( 4⋅4 )              =( 3⋅4 )( 3⋅4 )              = 12 2

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