# How do you simplify (x^(5/3)y)/(xy^(-1/2))?

Sep 19, 2016

$\textcolor{g r e e n}{{x}^{\frac{2}{3}} {y}^{\frac{3}{2}}}$

#### Explanation:

$\frac{{x}^{\frac{5}{3}} y}{x {y}^{- \frac{1}{2}}}$
$\textcolor{w h i t e}{\text{XXX}} = \frac{{x}^{\frac{5}{3}}}{x} \cdot \frac{y}{{y}^{- \frac{1}{2}}}$

$\textcolor{w h i t e}{\text{XXX}} = \left({x}^{\frac{5}{3}} \cdot {x}^{- 1}\right) \cdot \left(y \cdot {y}^{\frac{1}{2}}\right)$

$\textcolor{w h i t e}{\text{XXX}} = {x}^{\frac{2}{3}} \cdot {y}^{\frac{3}{2}}$

Sep 19, 2016

Just for comparison to Alan's

$\textcolor{m a r \infty n}{{x}^{\frac{2}{3}} {y}^{\frac{3}{2}}}$

#### Explanation:

Given:$\text{ } \frac{{x}^{\frac{5}{3}} y}{x {y}^{- \frac{1}{2}}}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Write as: $\text{ } \frac{\sqrt[3]{{x}^{3} \times {x}^{2}} \textcolor{w h i t e}{. .} y \sqrt{y}}{x}$

" "(cancel(x)^1root(3)(x^2)color(white)(..)ysqrt(y))/(cancel(x)^1

$\sqrt[3]{{x}^{2}} \times \sqrt{{y}^{2} \times y}$

${x}^{\frac{2}{3}} \times {y}^{\frac{3}{2}}$

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