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:

${\left({5}^{3}\right)}^{4}=\left({5}^{3}\right)\left({5}^{3}\right)\left({5}^{3}\right)\left({5}^{3}\right)$

But the product of powers property tells us that

${\left({5}^{3}\right)}^{4}=\left({5}^{3}\right)\left({5}^{3}\right)\left({5}^{3}\right)\left({5}^{3}\right)={5}^{3+3+3+3}={5}^{4\left(3\right)}={5}^{12}$

So it is enough to just multiply the powers!

In general,

${\left({a}^{b}\right)}^{c}={a}^{bc}$ .