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

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

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expand ((x/y)^{1/4})/((y/x)^{3/4)}

expand

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

\frac{x}{y}

Solution steps

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

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

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

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

= \frac{\frac{x ^{\frac{1}{4}}}{y ^{\frac{1}{4}}}}{\frac{y ^{\frac{3}{4}}}{x ^{\frac{3}{4}}}}

Divide fractions:

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

= \frac{x ^{\frac{1}{4}} x ^{\frac{3}{4}}}{y ^{\frac{1}{4}} y ^{\frac{3}{4}}}

x^{\frac{1}{4}} x^{\frac{3}{4}} = x^{\frac{1}{4} + \frac{3}{4}}

= \frac{x ^{\frac{1}{4} + \frac{3}{4}}}{y ^{\frac{1}{4}} y ^{\frac{3}{4}}}

y^{\frac{1}{4}} y^{\frac{3}{4}} = y^{\frac{1}{4} + \frac{3}{4}}

= \frac{x ^{\frac{1}{4} + \frac{3}{4}}}{y ^{\frac{1}{4} + \frac{3}{4}}}

Combine the fractions

\frac{1}{4} + \frac{3}{4} : 1

= \frac{x ^{\frac{1}{4} + \frac{3}{4}}}{y ^{1}}

Combine the fractions

\frac{1}{4} + \frac{3}{4} : 1

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

Apply rule

a^{1} = a

x^{1} = x, y^{1} = y

= \frac{x}{y}

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