What is (x^{2/3}y)(x^{-2}y)^{1/2} ?

The solution to (x^{2/3}y)(x^{-2}y)^{1/2} is (y^{3/2})/(x^{1/3)}

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simplify (x^{2/3}y)(x^{-2}y)^{1/2}

simplify

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

\frac{y ^{\frac{3}{2}}}{x ^{\frac{1}{3}}}

Solution steps

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

Simplify

(x^{- 2} y)^{\frac{1}{2}} : \frac{y ^{\frac{1}{2}}}{x}

= x^{\frac{2}{3}} y \frac{y ^{\frac{1}{2}}}{x}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x ^{\frac{2}{3}} y y ^{\frac{1}{2}}}{x}

Simplify

\frac{x ^{\frac{2}{3}}}{x} : \frac{1}{x ^{\frac{1}{3}}}

= \frac{y y ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}

Simplify

y y^{\frac{1}{2}} : y^{\frac{3}{2}}

= \frac{y ^{\frac{3}{2}}}{x ^{\frac{1}{3}}}

\frac{6 4 ^{\frac{5}{9}} \cdot 6 4 ^{\frac{2}{9}}}{4 ^{\frac{3}{4}}}

\frac{- 1}{4} (- 8 r) = \frac{- 1}{4} (- 36)

\frac{1}{16.62 + 3} + \frac{1}{16.62}

3 x^{2} + 3 x - 4 = 0

What is (x^{2/3}y)(x^{-2}y)^{1/2} ?
The solution to (x^{2/3}y)(x^{-2}y)^{1/2} is (y^{3/2})/(x^{1/3)}