Question

Simplify:
$\sqrt[12]({x {}^{4})} \frac{1}{3}$
​

Answer 1

The given expression can be written as,

$x^{4*\frac{1}{3}*\frac{1}{12} }$

$x^{\frac{1}{3}* \frac{1}{3} }$

$x^{\frac{1}{9} }$

= $\sqrt[9]{x}$

Answer 2

Step-by-step explanation:

$\bf \underline{Given-}$

$\sf{\sqrt[12]{( {x}^{4} {)}^{ \frac{1}{3} } } }$

$\bf \underline{To\: find-}$

$\textsf{the value of X = ? }$

$\bf \underline{Solution-}$

$\textsf{We have,}$

$\sf{\sqrt[12]{( {x}^{4} {)}^{ \frac{1}{3} } } }$

$\sf{ \Rightarrow \: \sqrt[12]{ {x}^{4 \times \frac{1}{3} } } }$

$\sf{ \Rightarrow \: \bigg( {x}^{ \frac{4}{3} } \bigg) ^{ \frac{1}{12} }}$

$\sf{ \Rightarrow \: {x}^{ \frac{ \cancel{4}}{3} \times \frac{1}{ \cancel{ {12 }^{3} }} } }$

$\sf{ \Rightarrow \: {x}^{ \frac{1}{3 \times 3} } }$

$\sf{ \Rightarrow \: {x}^{ \frac{1}{9} } }$

$\bf \underline{Answer-}$

$\underline{ \bf{Hence, the \: value \: of \: X \: is \: {x}^{ \frac{1}{9} } }}.$