What is ((y^2x^2)/(z^2))^4((y^2)/(x^2))^{-3} ?

The solution to ((y^2x^2)/(z^2))^4((y^2)/(x^2))^{-3} is (y^2x^{14})/(z^8)

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simplify ((y^2x^2)/(z^2))^4((y^2)/(x^2))^{-3}

simplify

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

\frac{y ^{2} x ^{14}}{z ^{8}}

Solution steps

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

Simplify

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

= \frac{y ^{8} x ^{8}}{z ^{8}} (\frac{y ^{2}}{x ^{2}})^{- 3}

Simplify

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

= \frac{y ^{8} x ^{8}}{z ^{8}} \cdot \frac{x ^{6}}{y ^{6}}

Apply the fraction rule:

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

= \frac{y ^{8} x ^{8} x ^{6}}{z ^{8} y ^{6}}

Simplify

\frac{y ^{8}}{y ^{6}} : y^{2}

= \frac{y ^{2} x ^{8} x ^{6}}{z ^{8}}

Simplify

x^{8} x^{6} : x^{14}

= \frac{y ^{2} x ^{14}}{z ^{8}}

8 (- 2)

\frac{4}{3} - \frac{1}{6}

(2 x - 4) - (6 x + 6)

9 x^{9}

\frac{x}{- x}

What is ((y^2x^2)/(z^2))^4((y^2)/(x^2))^{-3} ?
The solution to ((y^2x^2)/(z^2))^4((y^2)/(x^2))^{-3} is (y^2x^{14})/(z^8)