# How do you simplify (9 sqrt(50x^2)) / (3 sqrt(2x^4))?

Apr 14, 2016

$\frac{15}{x}$

#### Explanation:

$1$. Start by factoring out $3$ from the numerator and denominator.

(9sqrt(50x^2))/(3(sqrt(2x^4))

$= \frac{3 \left(3 \sqrt{50 {x}^{2}}\right)}{3 \left(\sqrt{2 {x}^{4}}\right)}$

$= \frac{3 \sqrt{50 {x}^{2}}}{\sqrt{2 {x}^{4}}}$

$2$. Multiply the numerator and denominator by $\sqrt{2 {x}^{4}}$ to get rid of the radical in the denominator.

$= \frac{3 \sqrt{50 {x}^{2}}}{\sqrt{2 {x}^{4}}} \left(\frac{\sqrt{2 {x}^{4}}}{\sqrt{2 {x}^{4}}}\right)$

$3$. Simplify.

$= \frac{3 \sqrt{100 {x}^{6}}}{2 {x}^{4}}$

$= \frac{3 \cdot 10 \sqrt{{x}^{6}}}{2 {x}^{4}}$

$= \frac{3 \cdot 5 {x}^{6 \left(\frac{1}{2}\right)}}{x} ^ 4$

$= \frac{15 {x}^{3}}{x} ^ 4$

$3$. Use the exponent quotient law, ${\textcolor{p u r p \le}{b}}^{\textcolor{red}{m}} \div {\textcolor{p u r p \le}{b}}^{\textcolor{b l u e}{n}} = {\textcolor{p u r p \le}{b}}^{\textcolor{red}{m} - \textcolor{b l u e}{n}}$, to simplify ${x}^{3} / {x}^{4}$.

$= 15 {x}^{3 - 4}$

$= 15 {x}^{-} 1$

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \frac{15}{x} \textcolor{w h i t e}{\frac{a}{a}} |}}}$