Power of a Power Property

To find a power of a power, multiply the exponents.  This is an extension of the product of powers property. Suppose you have a number raised to a power, and you multiply the whole expression by itself over and over. This is the same as raising the expression to a power:

( 5 3 ) 4 =( 5 3 )( 5 3 )( 5 3 )( 5 3 )

But the product of powers property tells us that

( 5 3 ) 4 =( 5 3 )( 5 3 )( 5 3 )( 5 3 )= 5 3+3+3+3 = 5 4( 3 ) = 5 12

So it is enough to just multiply the powers!

In general,

( a b ) c = a bc .