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

The solution to (x^{-4}+x^2y^{-3})/((xy)^{-2)} is (y^3+x^6)/(x^2y)

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

simplify

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

\frac{y ^{3} + x ^{6}}{x ^{2} y}

Solution steps

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

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

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

x^{2} y^{- 3} = \frac{x ^{2}}{y ^{3}}

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

Apply the fraction rule:

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

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

Join

x^{- 4} + \frac{x ^{2}}{y ^{3}} : \frac{y ^{3} + x ^{6}}{x ^{4} y ^{3}}

= \frac{\frac{x ^{6} + y ^{3}}{x ^{4} y ^{3}} x ^{2} y ^{2}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= \frac{y ^{3} + x ^{6}}{x ^{4} y ^{3}} x^{2} y^{2}

Multiply fractions:

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

= \frac{( y ^{3} + x ^{6} ) x ^{2} y ^{2}}{x ^{4} y ^{3}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

= \frac{y ^{2} ( x ^{6} + y ^{3} )}{y ^{3} x ^{4 - 2}}

Subtract the numbers:

4 - 2 = 2

= \frac{y ^{2} ( x ^{6} + y ^{3} )}{x ^{2} y ^{3}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{y ^{2}}{y ^{3}} = \frac{1}{y ^{3 - 2}}

= \frac{y ^{3} + x ^{6}}{x ^{2} y ^{3 - 2}}

Subtract the numbers:

3 - 2 = 1

= \frac{y ^{3} + x ^{6}}{x ^{2} y}

16 x^{2} - 32 x + 16

\frac{3}{5} t = - 12

(6 v)^{2}

4 (- 3)^{3}

What is (x^{-4}+x^2y^{-3})/((xy)^{-2)} ?
The solution to (x^{-4}+x^2y^{-3})/((xy)^{-2)} is (y^3+x^6)/(x^2y)