Question

{(\frac{2}{3})^{2} }" alt="\sqrt[6]{(\frac{2}{3})^{2} }" align="absmiddle" class="latex-formula"> as a power

Answer 1

Answer:

$\frac{2}{3}^{\frac{1}{3}}$

Step-by-step explanation:

The n-th root is the same thing as the denominator of an exponent.

For example. $\sqrt[3]{x} = x^{\frac{1}{3}}$

and $\sqrt[4]{x} = x^{\frac{1}{4}}$

and $\sqrt{x} = x^{\frac{1}{2}}$

So

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