How do you simplify 7^{2} × 7^{6}?

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:

7^{8}

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

7^{2} ×
7^{6} = 7^{(2 + 6) }= 7^{8}

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

*a ^{b}* ×

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