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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

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

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

Apply the fraction rule:

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

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

(7 + h)^{3}

\frac{5 x + 4 y}{6} + \frac{3 x - y}{2}

49 x^{5}

\frac{20 x ^{24}}{10 x ^{6}}

1 + 3.3 \cdot lo g_{10} (50)

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