Question

use radical notation to write the expression. simplify if possible. assume that all variables represent positive n
$(3x)^{\frac{2}{3}}$
$(3x)^{\frac{2}{3}}=\square$

Explanation:

Step1: Apply exponent to radical rule

Recall $a^{\frac{m}{n}} = \sqrt[n]{a^m}$. For $(3x)^{\frac{2}{3}}$, $a=3x$, $m=2$, $n=3$.
$$(3x)^{\frac{2}{3}} = \sqrt[3]{(3x)^2}$$

Step2: Simplify the radicand

Expand $(3x)^2$ using exponent rules.
$$\sqrt[3]{(3x)^2} = \sqrt[3]{9x^2}$$

Answer:

$\sqrt[3]{9x^2}$