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:

( 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 × a c = a ( b + c )

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