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 7 s, 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 with the same base, add the exponents.