What is ((x^{1/2}y^{-2})/(yx^{-7/4)})^4 ?

The solution to ((x^{1/2}y^{-2})/(yx^{-7/4)})^4 is (x^9)/(y^{12)}

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simplify ((x^{1/2}y^{-2})/(yx^{-7/4)})^4

simplify

(\frac{x ^{\frac{1}{2}} y ^{- 2}}{y x ^{- \frac{7}{4}}})^{4}

\frac{x ^{9}}{y ^{12}}

Solution steps

(\frac{x ^{\frac{1}{2}} y ^{- 2}}{y x ^{- \frac{7}{4}}})^{4}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( x ^{\frac{1}{2}} y ^{- 2} ) ^{4}}{( y x ^{- \frac{7}{4}} ) ^{4}}

Simplify

(x^{\frac{1}{2}} y^{- 2})^{4} : \frac{x ^{2}}{y ^{8}}

= \frac{\frac{x ^{2}}{y ^{8}}}{( y x ^{- \frac{7}{4}} ) ^{4}}

Simplify

(y x^{- \frac{7}{4}})^{4} : \frac{y ^{4}}{x ^{7}}

= \frac{\frac{x ^{2}}{y ^{8}}}{\frac{y ^{4}}{x ^{7}}}

Divide fractions:

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

= \frac{x ^{2} x ^{7}}{y ^{8} y ^{4}}

x^{2} x^{7} = x^{9}

= \frac{x ^{9}}{y ^{8} y ^{4}}

y^{8} y^{4} = y^{12}

= \frac{x ^{9}}{y ^{12}}

\frac{( x + 9 ) ( x - 11 )}{x + 7} \leq 0

6 x - 3 = 7 x - 11

4 y^{2} - 9

2 x y^{4} (11 x^{5} y^{5})

- 34 = 8 x - 15

What is ((x^{1/2}y^{-2})/(yx^{-7/4)})^4 ?
The solution to ((x^{1/2}y^{-2})/(yx^{-7/4)})^4 is (x^9)/(y^{12)}