Answer:
Rewriting the expression [tex](3^\frac{2}{3})^\frac{1}{6}[/tex] with a rational exponent as a radical expression we get [tex]\mathbf{\sqrt[9]{3} }[/tex]
Step-by-step explanation:
We need to rewrite the expression [tex](3^\frac{2}{3})^\frac{1}{6}[/tex] with a rational exponent as a radical expression.
The expression given is:
[tex](3^\frac{2}{3})^\frac{1}{6}[/tex]
First we will simply the expression using exponent rule [tex](a^m)^n=a^{mn}[/tex]
[tex](3^\frac{2}{3})^\frac{1}{6}\\=(3^\frac{2}{18})[/tex]
As we know 2 and 18 are both divisible by 2, we can write
[tex]=(3^\frac{1}{9})[/tex]
Now we know that [tex]a^\frac{1}{9}=\sqrt[9]{a}[/tex]
Using this we get
[tex]=\sqrt[9]{3}[/tex]
So, rewriting the expression [tex](3^\frac{2}{3})^\frac{1}{6}[/tex] with a rational exponent as a radical expression we get [tex]\mathbf{\sqrt[9]{3} }[/tex]
