# How do you simplify (100x^3y^5)/(36xy^8)?

May 19, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\frac{100}{36} \left({x}^{3} / x\right) \left({y}^{5} / {y}^{8}\right) \implies \frac{4 \times 25}{4 \times 9} \left({x}^{3} / x\right) \left({y}^{5} / {y}^{8}\right) \implies$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times 25}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times 9} \left({x}^{3} / x\right) \left({y}^{5} / {y}^{8}\right) \implies \frac{25}{9} \left({x}^{3} / x\right) \left({y}^{5} / {y}^{8}\right)$

Next, use these two rules of exponents to simplify the $x$ terms:

$a = {a}^{\textcolor{b l u e}{1}}$ and ${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$

$\frac{25}{9} \left({x}^{3} / x\right) \left({y}^{5} / {y}^{8}\right) \implies \frac{25}{9} \left({x}^{\textcolor{red}{3}} / {x}^{\textcolor{b l u e}{1}}\right) \left({y}^{5} / {y}^{8}\right) \implies \frac{25}{9} {x}^{\textcolor{red}{3} - \textcolor{b l u e}{1}} \left({y}^{5} / {y}^{8}\right) \implies$

$\frac{25 {x}^{2}}{9} \left({y}^{5} / {y}^{8}\right)$

Now, use this rule of exponents to simplify the $y$ term:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = \frac{1}{x} ^ \left(\textcolor{b l u e}{b} - \textcolor{red}{a}\right)$

$\frac{25 {x}^{2}}{9} \left({y}^{\textcolor{red}{5}} / {y}^{\textcolor{b l u e}{8}}\right) \implies \frac{25 {x}^{2}}{9} \cdot \frac{1}{y} ^ \left(\textcolor{b l u e}{8} - \textcolor{red}{5}\right) \implies \frac{25 {x}^{2}}{9} \cdot \frac{1}{y} ^ 3 \implies$

$\frac{25 {x}^{2}}{9 {y}^{3}}$