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 the 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?

Open in App

Solution

${(\frac{9 a^{3} b^{- 8}}{81 a^{- 5} b^{2}})}^{- \frac{1}{2}}$
$= {(\frac{a^{3 - (- 5)} b^{- 8 - 2}}{9})}^{- \frac{1}{2}}$
$= {(\frac{a^{8} b^{- 10}}{3^{2}})}^{- \frac{1}{2}}$
$= {[\frac{(a^{4} b^{- 5})^{2}}{3^{2}}]}^{- \frac{1}{2}}$
$= {[{(\frac{a^{4} b^{- 5}}{3})}^{2}]}^{- \frac{1}{2}}$
$= {(\frac{a^{4} b^{- 5}}{3})}^{2 \times - \frac{1}{2}}$
$= (3^{- 1} a^{4} b^{- 5})^{- 1}$
$= 3^{- 1 \times - 1} a^{4 \times - 1} b^{- 5 \times - 1}$
$= 3 a^{- 4} b^{5} = \frac{3 b^{5}}{a^{4}}$

So, both of them are correct

Suggest Corrections

Similar questions

Q. 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?

tinu wrote the answer of (x+8) divided by 8 as (x+1) and mary wrote it as x tinu found that both were wrong how justify your answer

A teacher wrote a large number on the board and asked the students to tell about the divisors of the number of. The students said that the number was divisible by numbers from 2 to 31.The teacher said that two students answered wrongly if taken that each student told one number in order.Which two students answered wrongly?i

Raj asked his son to write $3^{3} \times 8^{2}$ but he wrote $2000$ .Find the difference between the two.

Q. Three students Varun, Kartik and Sid wrote a statement on a blackboard.
Varun wrote, “Two rectangles are congruent, if they have same perimeter”.
Kartik wrote, “Two squares are congruent, if they have same area”.
Sid wrote, “Two circles are congruent, if they have same diameter”.
Who wrote the correct statement?

Join BYJU'S Learning Program

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

(9a3b−881a−5b2)−12 =(a3−(−5)b−8−29)−12 =(a8b−1032)−12 =[(a4b−5)232]−12 =[(a4b−53)2]−12 =(a4b−53)2×−12 =(3−1a4b−5)−1 =3−1×−1a4×−1b−5×−1 =3a−4b5=3b5a4 So, both of them are correct

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 the 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?