Question

x^1/2=8 then ( x^1/3 )^2=?​

Answer 1

Question:-

${x}^{ \frac{1}{2} } = 8 \: \: then \: {( {x}^{ \frac{1}{3} }) }^{2} =$

Useful formulae:-

$({ {a}^{m}) }^{n} = {a}^{mn}$

Solution:-

Given,

${x}^{ \frac{1}{2} } = 8$

$\sqrt{x} = 8$

Hence,

$x = {8}^{2} = 64equ(1)$

Simplify

$( { {x}^{ \frac{1}{3} } )}^{2} = {x}^{ \frac{1}{3} \times 2 }$

$= > {x}^{ \frac{2}{3} }$

Then,

${x}^{ \frac{2}{3} } = {64}^{ \frac{2}{3} } from(1)$

$= > {(4 \times 4 \times 4)}^{ \frac{2}{3} }$

${( {4}^{3} )}^{ \frac{2}{3} }$

$= > {4}^{2}$

$= > 16$

Final Solution:-

16

Answer 2

This is the correct answer.