Question

\sqrt [ 3 ] { ( \frac { 1 } { 64 } ) ^ { \frac { 1 } { 2 } } }​

Answer 1

Answer:

The solution is $\sqrt [ 3 ] { ( \frac { 1 } { 64 } ) ^ { \frac { 1 } { 2 } } }$ is $\frac{1}{2}$

Step-by-step explanation:

We know that $\sqrt{x}$ = $x^{\frac{1}{2} }$ and $\sqrt [ 3 ] { x } } }$ = $x^{\frac{1}{3} }$

Now, $\frac{1}{64}$ can be written as $(\frac{1}{2})^{6}$.

According to question,

⇒  $\sqrt [ 3 ] { ( \frac { 1 } { 64 } ) ^ { \frac { 1 } { 2 } } }$

⇒ $\sqrt [ 3 ] { ( \frac { 1 } { 2} )^{6}^ { \frac { 1 } { 2 } } }$

⇒ ${ ( \frac { 1 } { 2} )^{3 } } }^{\frac{1}{3} }$

⇒ $(\frac{1}{2})^{1}$

⇒ $\frac{1}{2}$