# Power of a Quotient Property

This is similar to the power of a product property . Suppose you're dividing two expressions with the same exponent, but different bases.

By canceling common factors, you can see that:

Example 1:

$\frac{{20}^{\text{\hspace{0.17em}}3}}{{4}^{\text{\hspace{0.17em}}3}}=\frac{5\cdot \overline{)4}\cdot 5\cdot \overline{)4}\cdot 5\cdot \overline{)4}}{\overline{)4}\cdot \overline{)4}\cdot \overline{)4}}={5}^{3}$

Example 2:

Simplify ${\left(\frac{a}{6}\right)}^{2}$ .

${\left(\frac{a}{6}\right)}^{2}=\frac{{a}^{\text{\hspace{0.17em}}2}}{{6}^{\text{\hspace{0.17em}}2}}=\frac{{a}^{\text{\hspace{0.17em}}6}}{36}$

For all real numbers $a,b$ and $c$ (as long as $b\ne 0$ , and $a$ and $c$ are not both $0$ ):

$\frac{{a}^{\text{\hspace{0.17em}}c}}{{b}^{\text{\hspace{0.17em}}c}}={\left(\frac{a}{b}\right)}^{c}$