Mr.Gupta asked two of his students to solve the expression ${(\frac{9 a^{3} b^{- 8}}{81 a^{- 5} b^{2}})}^{\frac{1}{2}}$ and write the answer on blackboard.Aryan wrote the answer as $3 a^{- 4} b^{5}$ whereas Ayan wrote the answer as $\frac{3 b^{5}}{a^{4}}$ .Who wrote the correct answer?

Aryan

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Ayan

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Both of them

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None of these

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Solution

The correct option is D Both of them
We have, $(\frac{9 a^{3} b^{* 8}}{81 a^{- 5} b^{2}})^{- \frac{1}{2}} = (\frac{81 a^{- 5} b^{2}}{9 a^{3} b^{- 8}})^{\frac{1}{2}}$
$= (9 a^{- 5} a^{- 3} b^{2} b^{8})^{\frac{1}{2}} = (9 a^{- 8} b^{10})^{\frac{1}{2}} = 3 a^{- 4} b^{5}$

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Mr.Gupta asked two of his students to solve the expression (9a3b−881a−5b2)12 and write the answer on blackboard.Aryan wrote the answer as 3a−4b5 whereas Ayan wrote the answer as 3b5a4.Who wrote the correct answer?

The correct option is D Both of themWe have,(9a3b∗881a−5b2)−12=(81a−5b29a3b−8)12=(9a−5a−3b2b8)12=(9a−8b10)12=3a−4b5

Mr.Gupta asked two of his students to solve the expression ${(\frac{9 a^{3} b^{- 8}}{81 a^{- 5} b^{2}})}^{\frac{1}{2}}$ and write the answer on blackboard.Aryan wrote the answer as $3 a^{- 4} b^{5}$ whereas Ayan wrote the answer as $\frac{3 b^{5}}{a^{4}}$ .Who wrote the correct answer?

The correct option is D Both of them
We have, $(\frac{9 a^{3} b^{* 8}}{81 a^{- 5} b^{2}})^{- \frac{1}{2}} = (\frac{81 a^{- 5} b^{2}}{9 a^{3} b^{- 8}})^{\frac{1}{2}}$
$= (9 a^{- 5} a^{- 3} b^{2} b^{8})^{\frac{1}{2}} = (9 a^{- 8} b^{10})^{\frac{1}{2}} = 3 a^{- 4} b^{5}$