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

The solution to ((x^2)/(y^{-2)})^{-2}((3y^{-3})/(x^2))^3 is (27)/(x^{10)y^{13}}

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

simplify

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

\frac{27}{x ^{10} y ^{13}}

Solution steps

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

Simplify

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

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

Simplify

(\frac{3 y ^{- 3}}{x ^{2}})^{3} : \frac{27}{x ^{6} y ^{9}}

= \frac{1}{x ^{4} y ^{4}} \cdot \frac{27}{x ^{6} y ^{9}}

Apply the fraction rule:

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

= \frac{1 \cdot 27}{x ^{4} y ^{4} x ^{6} y ^{9}}

Multiply the numbers:

1 \cdot 27 = 27

= \frac{27}{x ^{4} y ^{4} x ^{6} y ^{9}}

Simplify

x^{4} y^{4} x^{6} y^{9} : x^{10} y^{13}

= \frac{27}{x ^{10} y ^{13}}

\frac{x ^{2} \cdot 1}{3 ( x ^{5} )}

2 cos^{2} (5 x) - 1

(a - b)^{3} + (b - c)^{3} + (c - a)^{3}

a (a + b)^{3} - 3 a^{2} b (a + b)

9 x^{2} + 6 x + 1 - 25 y^{2}

What is ((x^2)/(y^{-2)})^{-2}((3y^{-3})/(x^2))^3 ?
The solution to ((x^2)/(y^{-2)})^{-2}((3y^{-3})/(x^2))^3 is (27)/(x^{10)y^{13}}