Answer
a.) $\sqrt[2]{x} $
b.) $3x^2$
Work Step by Step
$\textbf{Part A.}$
To determine the value of the expression use the rule: $\sqrt[n]{a^m} = a^{m/n}$
\begin{aligned}\sqrt[6]{x^3}&= x^{3/6}\\
&= x^{1/2}\\
&= \sqrt[2]{x}
\end{aligned}
The value of the given expression is:
$$\sqrt[2]{x} $$
$\textbf{Part B.}$
To determine the value of the expression use the rule: $\sqrt[n]{a^m} = a^{m/n}$
\begin{aligned}\sqrt[4]{(3x^2)^4} &= \sqrt[4]{(3x^2)^4} \\
&=(3x^2)^{4/4}\\
&=(3x^2)^1\\
&=3x^2\end{aligned}
The value of the given expression is:
$$3x^2$$
