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

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

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

simplify

(x^{- 2} + y^{- 2})^{- 1}

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

Solution steps

(x^{- 2} + y^{- 2})^{- 1}

Apply exponent rule:

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

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

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

Simplify

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

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

Join

\frac{1}{x ^{2}} + \frac{1}{y ^{2}} : \frac{y ^{2} + x ^{2}}{x ^{2} y ^{2}}

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

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

2 x^{2} + x - 4 - ∣ 2 x ∣ = 0

\frac{14 k ^{3} + 7 k ^{2}}{7 k ^{3} + 14 k ^{2}}

s^{2} - 2 s + 2 = 0

5 \leq 3 y + 8 < 17

x^{4} - x^{3} - x^{2} - x - 2

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