Question

Rewrite the expression with a rational exponent as a radical expression.

Answer 1

Answer:

Rewriting the expression $(3^\frac{2}{3})^\frac{1}{6}$ with a rational exponent as a radical expression we get $\mathbf{\sqrt[9]{3} }$

Step-by-step explanation:

We need to rewrite the expression $(3^\frac{2}{3})^\frac{1}{6}$ with a rational exponent as a radical expression.

The expression given is:

$(3^\frac{2}{3})^\frac{1}{6}$

First we will simply the expression using exponent rule $(a^m)^n=a^{mn}$

$(3^\frac{2}{3})^\frac{1}{6}\\=(3^\frac{2}{18})$

As we know 2 and 18 are both divisible by 2, we can write

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

Now we know that $a^\frac{1}{9}=\sqrt[9]{a}$

Using this we get

$=\sqrt[9]{3}$

So, rewriting the expression $(3^\frac{2}{3})^\frac{1}{6}$ with a rational exponent as a radical expression we get $\mathbf{\sqrt[9]{3} }$