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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 having the same base, add the exponents.