Product of Powers Property

How do you simplify 72 × 76?

If you recall the way exponents are defined, you know that this means:

(7 × 7) × (7 × 7 × 7 × 7 × 7 × 7)

If we remove the parentheses, we have the product of eight 7s, which can be written more simply as:

78

This suggests a shortcut: all we need to do is add the exponents!

72 × 76 = 7(2 + 6) = 78

In general, for all real numbers a, b, and c,

ab × ac = a(b + c)

To multiply two powers with the same base, add the exponents.