# How do evaluate \frac { 15x ^ { 14} y ^ { 14} } { 3x ^ { 6} y ^ { 2} }?

Mar 5, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\left(\frac{15}{3}\right) \left({x}^{14} / {x}^{6}\right) \left({y}^{14} / {y}^{2}\right) \implies$

$5 \left({x}^{14} / {x}^{6}\right) \left({y}^{14} / {y}^{2}\right)$

Now, use this rule of exponents to complete the simplification:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$

$5 \left({x}^{\textcolor{red}{14}} / {x}^{\textcolor{b l u e}{6}}\right) \left({y}^{\textcolor{red}{14}} / {y}^{\textcolor{b l u e}{2}}\right) \implies$

$5 {x}^{\textcolor{red}{14} - \textcolor{b l u e}{6}} {y}^{\textcolor{red}{14} - \textcolor{b l u e}{2}} \implies$

$5 {x}^{8} {y}^{12}$