Question

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

Answer 1

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.
$9^{\frac{2}{3}}$
$=(3^{2})^{\frac{2}{3}}$
$=3^{\frac{4}{3}}$

Second, change into radical form
The denominator of fractional exponent is the root of the radical
$3^{\frac{4}{3}}$
$= \sqrt[3]{ 3^{4}}$

Third, simplify the exponential form under the radical using exponential property
$= \sqrt[3]{ 3^{3+1}}$
$= \sqrt[3]{3^{3} \times 3^{1}}$
$= \sqrt[3]{3^{3}} \times \sqrt[3]{3}$
$= 3 \times \sqrt[3]{3}$
$= 3 \sqrt[3]{3}$

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

Answer 2

Answer:3

Step-by-step explanation: