How do you simplify (x^{\frac{1}{2}} y^{-\frac{2}{3}})(x^2 y^{\frac{1}{3}})?

Nov 13, 2014

$\left({x}^{\frac{1}{2}} {y}^{- \frac{2}{3}}\right) \left({x}^{2} {y}^{\frac{1}{3}}\right)$

by grouping the factors with the same bases,

$= \left({x}^{\frac{1}{2}} \cdot {x}^{2}\right) \left({y}^{- \frac{2}{3}} \cdot {y}^{\frac{1}{3}}\right)$

by ${b}^{x} \cdot {b}^{y} = {b}^{x + y}$,

$= {x}^{\frac{1}{2} + 2} \cdot {y}^{- \frac{2}{3} + \frac{1}{3}} = {x}^{\frac{5}{2}} \cdot {y}^{- \frac{1}{3}}$

by ${b}^{- x} = \frac{1}{b} ^ x$,

$= {x}^{\frac{5}{2}} / {y}^{\frac{1}{3}} = \frac{\sqrt{{x}^{5}}}{\sqrt[3]{y}}$

I hope that this was helpful.