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

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

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

simplify

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

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

Solution steps

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

Simplify

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

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

Simplify

(b^{\frac{1}{2}})^{2} : b

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

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