Question

When 9 and 2/3 is written in simplest radical form, which value remains under the radical?36927

Answer 1

Given

$9^{\frac{2}{3}}$

To write it in the simplest form and to find which value remains under the radical.

Explanation:

It is given that,

$9^{\frac{2}{3}}$

It is known that,

$x^{\frac{m}{n}}=\sqrt[n]{x^m}$

That implies,

$\begin{gathered} 9^{\frac{2}{3}}=\sqrt[3]{9^2} \\ =\sqrt[3]{3\times3\times3\times3} \\ =3\sqrt[3]{3} \end{gathered}$

Therefore, the simplest form of the expression is,

$3\sqrt[3]{3}$

and the value that remains under the radical is 3.