What is ((x^2y)^{-1/3}(xy)^{1/4})/((xy^{-2))^{1/12}} ?

The solution to ((x^2y)^{-1/3}(xy)^{1/4})/((xy^{-2))^{1/12}} is (y^{1/12})/(x^{1/2)}

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simplify ((x^2y)^{-1/3}(xy)^{1/4})/((xy^{-2))^{1/12}}

simplify

\frac{( x ^{2} y ) ^{- \frac{1}{3}} ( x y ) ^{\frac{1}{4}}}{( x y ^{- 2} ) ^{\frac{1}{12}}}

\frac{y ^{\frac{1}{12}}}{x ^{\frac{1}{2}}}

Solution steps

\frac{( x ^{2} y ) ^{- \frac{1}{3}} ( x y ) ^{\frac{1}{4}}}{( x y ^{- 2} ) ^{\frac{1}{12}}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(x y)^{\frac{1}{4}} = x^{\frac{1}{4}} y^{\frac{1}{4}}

= \frac{( x ^{2} y ) ^{- \frac{1}{3}} x ^{\frac{1}{4}} y ^{\frac{1}{4}}}{( x y ^{- 2} ) ^{\frac{1}{12}}}

Simplify

(x y^{- 2})^{\frac{1}{12}} : x^{\frac{1}{12}} \frac{1}{y ^{\frac{1}{6}}}

= \frac{( x ^{2} y ) ^{- \frac{1}{3}} x ^{\frac{1}{4}} y ^{\frac{1}{4}}}{x ^{\frac{1}{12}} \frac{1}{y ^{\frac{1}{6}}}}

Simplify

\frac{x ^{\frac{1}{4}}}{x ^{\frac{1}{12}}} : x^{\frac{1}{6}}

= \frac{( x ^{2} y ) ^{- \frac{1}{3}} x ^{\frac{1}{6}} y ^{\frac{1}{4}}}{\frac{1}{y ^{\frac{1}{6}}}}

Simplify

\frac{( x ^{2} y ) ^{- \frac{1}{3}} x ^{\frac{1}{6}} y ^{\frac{1}{4}}}{\frac{1}{y ^{\frac{1}{6}}}} : \frac{y ^{\frac{1}{12}}}{x ^{\frac{1}{2}}}

= \frac{y ^{\frac{1}{12}}}{x ^{\frac{1}{2}}}

1 \cdot \frac{1}{197.927} \cdot \frac{2}{4} \cdot 159.69

2 x^{3} + 18 x^{2} + 66 x + 50

4 x^{3} - 12 y^{4}

x^{2} - 8 x + 12 \leq 0

v^{2} - 8 v + 16

What is ((x^2y)^{-1/3}(xy)^{1/4})/((xy^{-2))^{1/12}} ?
The solution to ((x^2y)^{-1/3}(xy)^{1/4})/((xy^{-2))^{1/12}} is (y^{1/12})/(x^{1/2)}