What is (a^{-2}+b^{-2})^{-1} ?

The solution to (a^{-2}+b^{-2})^{-1} is (a^2b^2)/(b^2+a^2)

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simplify (a^{-2}+b^{-2})^{-1}

simplify

(a^{- 2} + b^{- 2})^{- 1}

\frac{a ^{2} b ^{2}}{b ^{2} + a ^{2}}

Solution steps

(a^{- 2} + b^{- 2})^{- 1}

Apply exponent rule:

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

(a^{- 2} + b^{- 2})^{- 1} = \frac{1}{a ^{- 2} + b ^{- 2}}

= \frac{1}{a ^{- 2} + b ^{- 2}}

Simplify

a^{- 2} + b^{- 2} : \frac{1}{a ^{2}} + \frac{1}{b ^{2}}

= \frac{1}{\frac{1}{a ^{2}} + \frac{1}{b ^{2}}}

Join

\frac{1}{a ^{2}} + \frac{1}{b ^{2}} : \frac{b ^{2} + a ^{2}}{a ^{2} b ^{2}}

= \frac{1}{\frac{b ^{2} + a ^{2}}{a ^{2} b ^{2}}}

Apply the fraction rule:

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

= \frac{a ^{2} b ^{2}}{b ^{2} + a ^{2}}

2 x^{2} = 10 x

5^{4} \cdot 5^{3}

a \frac{4}{7}

\frac{1225 π}{8} \cdot \frac{1024}{3}

6 x^{4} + 5 x^{2} - 6

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