Question

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

Answer 1

3

Explanation:

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

Answer 2

The value remains under the radical is 3.

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^{(2)/(3)}`

We re-write the expression as,

`9^{(2)/(3)}=(9^2)^{(1)/(3)}`

`9^{(2)/(3)}=\sqrt[3]{9^2}`

`9^{(2)/(3)}=\sqrt[3]{81}`

`9^{(2)/(3)}=\sqrt[3]{3* 3* 3* 3}`

`9^{(2)/(3)}=3\sqrt[3]{3}`

Therefore, the value remains under the radical is 3.