Question

When 9 Superscript two-thirds is written in simplest radical form, which value remains under the radical?

Answer 1

Answer:

  3

Step-by-step explanation:

$9^{\frac{2}{3}}=(3^2)^{\frac{2}{3}}=3^{\frac{4}{3}}=3\cdot 3^{\frac{1}{3}}\\\\=3\sqrt[3]{3}$

Answer 2

Answer:

The value remains under the radical is 3.

Step-by-step explanation:

Given : When 9 Superscript two-thirds is written in simplest radical form.

To find : Which value remains under the radical?

Solution :

The expression given 9 Superscript two-thirds is written as,

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

We re-write the expression as,  

$9^{\frac{2}{3}}=(9^2)^{\frac{1}{3}}$

$9^{\frac{2}{3}}=\sqrt[3]{9^2}$

$9^{\frac{2}{3}}=\sqrt[3]{81}$

$9^{\frac{2}{3}}=\sqrt[3]{3\times 3\times 3\times 3}$

$9^{\frac{2}{3}}=3\sqrt[3]{3}$

Therefore, the value remains under the radical is 3.