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.
