# Product of Powers Property

How do you simplify ${7}^{2}×{7}^{6}$ ?

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

$\left(7×7\right)×\left(7×7×7×7×7×7\right)$

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

${7}^{8}$

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

${7}^{2}×{7}^{6}={7}^{\left(2 + 6\right)}={7}^{8}$

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

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