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 = am · bm.

Example 1:

Simplify (3t)4

(3t)4 = 34 · t4 = 81t4

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

         am · bm = (ab)m.

Example 2:

Simplify 32 · 42

32 · 42 = (3 · 3) · (4 · 4)

           = (3 · 4) (3 · 4)

           = 122

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