Question

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

Answer 1

Answer:3

Explanation:

Answer 2

First, change 9 into exponential form. 9 equals 3 squared. We change 9 into smaller number to find the simplest form of the radical later.

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

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

`=3^{(4)/(3)}`

Second, change into radical form
The denominator of fractional exponent is the root of the radical

`3^{(4)/(3)}`

`= \sqrt[3]{ 3^(4)}`

Third, simplify the exponential form under the radical using exponential property

`= \sqrt[3]{ 3^(3+1)}`

`= \sqrt[3]{3^(3) * 3^(1)}`

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

`= 3 * \sqrt[3]{3}`

`= 3 \sqrt[3]{3}`

In the simplest radical form, what remains under the radical is 3