# How do you simplify sqrt(3x^2y^3)/(4sqrt(5xy^3))?

May 21, 2017

See a solution process below:

#### Explanation:

We can use this rule for dividing radicals to rewrite this expression:

$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$

$\frac{\sqrt{3 {x}^{2} {y}^{3}}}{4 \sqrt{5 x {y}^{3}}} \implies \frac{1}{4} \sqrt{\frac{3 {x}^{2} {y}^{3}}{5 x {y}^{3}}} \implies \frac{1}{4} \sqrt{\frac{3 {x}^{2} \textcolor{red}{\cancel{\textcolor{b l a c k}{{y}^{3}}}}}{5 x \textcolor{red}{\cancel{\textcolor{b l a c k}{{y}^{3}}}}}} \implies$

$\frac{1}{4} \sqrt{\frac{3 {x}^{2}}{5 x}}$

Next, we can use these rules of exponents to simplify the $x$ term:

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

$\frac{1}{4} \sqrt{\frac{3 {x}^{2}}{5 x}} \implies \frac{1}{4} \sqrt{\frac{3 {x}^{\textcolor{red}{2}}}{5 {x}^{\textcolor{b l u e}{1}}}} \implies \frac{1}{4} \sqrt{\frac{3 {x}^{\textcolor{red}{2} - \textcolor{b l u e}{1}}}{5}} \implies \frac{1}{4} \sqrt{\frac{3 {x}^{\textcolor{red}{1}}}{5}} \implies$

$\frac{1}{4} \sqrt{\frac{3 x}{5}}$