# How do you simplify (2sqrtx*sqrt(x^3))/sqrt(9x^10)?

Jan 16, 2018

See a solution process below:

#### Explanation:

First, we can take the square root of the term in the denominator giving:

$\frac{2 \sqrt{x} \cdot \sqrt{{x}^{3}}}{3 {x}^{5}}$

Next, we can use this rule of radicals to simplify the numerator:

$\sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}}$

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

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

We can now use this rule for exponents to simplify the $x$ terms:

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

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