# What is the quotient of powers property?

##### 1 Answer
Dec 19, 2014

$\frac{{a}^{m}}{{a}^{n}} = {a}^{m - n}$

This property allows you to simplify problems where you have a fraction of the same numbers ( $a$) raised to different powers ($m \mathmr{and} n$).
For example:

$\frac{{3}^{3}}{{3}^{2}} = \frac{3 \cdot 3 \cdot 3}{3 \cdot 3} = {3}^{3 - 2} = 3$

You can see how the power of 3, in the numerator, is "reduced" by the presence of the power 2 in the denominator.

You can also check te result by doing the multiplications:

$\frac{{3}^{3}}{{3}^{2}} = \frac{3 \cdot 3 \cdot 3}{3 \cdot 3} = \frac{27}{9} = 3$

As a challenge try to find out what happens when $m = n$ !!!!!