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:

(53)4 = (53)(53)(53)(53)

But the product of powers property tells us that

(53)(53)(53)(53) = 53 + 3 + 3 + 3 = 54(3) = 512

So it is enough to just multiply the powers!

In general,

(ab)c = abc