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

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

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

simplify

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

\frac{y ^{\frac{1}{2}}}{x ^{\frac{1}{4}}}

Solution steps

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

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

Simplify

(x^{2} y)^{\frac{3}{4}} : x^{\frac{3}{2}} y^{\frac{3}{4}}

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

Simplify

\frac{x ^{\frac{1}{4}}}{x ^{\frac{3}{2}}} : \frac{1}{x ^{\frac{5}{4}}}

= \frac{y ^{\frac{1}{4}} ( x ^{2} y ^{2} ) ^{\frac{1}{2}}}{x ^{\frac{5}{4}} y ^{\frac{3}{4}}}

Simplify

\frac{y ^{\frac{1}{4}}}{y ^{\frac{3}{4}}} : \frac{1}{y ^{\frac{1}{2}}}

= \frac{( x ^{2} y ^{2} ) ^{\frac{1}{2}}}{x ^{\frac{5}{4}} y ^{\frac{1}{2}}}

Simplify

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

= \frac{x y}{x ^{\frac{5}{4}} y ^{\frac{1}{2}}}

Simplify

\frac{x}{x ^{\frac{5}{4}}} : \frac{1}{x ^{\frac{1}{4}}}

= \frac{y}{x ^{\frac{1}{4}} y ^{\frac{1}{2}}}

Simplify

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

= \frac{y ^{\frac{1}{2}}}{x ^{\frac{1}{4}}}

z^{2} + 1 = 0

15 y^{2} + 31 y + 2

x - \frac{5 x}{4} + \frac{3}{4} = \frac{3 x}{8} - \frac{3 x}{2} - \frac{7}{8}

\frac{5}{1 - e ^{\frac{1}{- 0.1}}}

12 x^{2} = 0

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