Answer
$\sqrt{3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt[8]{3^4}
,$ use the definition of rational exponents.
$\bf{\text{Solution Details:}}$
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
3^{\frac{4}{8}}
.\end{array}
The expression above simplifies to
\begin{array}{l}\require{cancel}
3^{\frac{1}{2}}
\\\\=
\sqrt{3}
.\end{array}
