What is (x^{-1})/(x^{-2)+y^{-8}} ?

The solution to (x^{-1})/(x^{-2)+y^{-8}} is (xy^8)/(y^8+x^2)

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simplify (x^{-1})/(x^{-2)+y^{-8}}

simplify

\frac{x ^{- 1}}{x ^{- 2} + y ^{- 8}}

\frac{x y ^{8}}{y ^{8} + x ^{2}}

Solution steps

\frac{x ^{- 1}}{x ^{- 2} + y ^{- 8}}

Apply exponent rule:

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

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

= \frac{\frac{1}{x}}{x ^{- 2} + y ^{- 8}}

Simplify

x^{- 2} + y^{- 8} : \frac{y ^{8} + x ^{2}}{x ^{2} y ^{8}}

= \frac{\frac{1}{x}}{\frac{y ^{8} + x ^{2}}{x ^{2} y ^{8}}}

Apply the fraction rule:

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

= \frac{1 \cdot x ^{2} y ^{8}}{x ( y ^{8} + x ^{2} )}

Cancel

\frac{1 \cdot x ^{2} y ^{8}}{x ( y ^{8} + x ^{2} )} : \frac{x y ^{8}}{y ^{8} + x ^{2}}

= \frac{x y ^{8}}{y ^{8} + x ^{2}}

(\frac{3}{7})^{2} + (\frac{x}{7}) = 1

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6 w + 2 = 9 w + 14

4 - 7 z = 6 - 2 z

What is (x^{-1})/(x^{-2)+y^{-8}} ?
The solution to (x^{-1})/(x^{-2)+y^{-8}} is (xy^8)/(y^8+x^2)