Answer
$5^{3/8}$
Work Step by Step
Using the laws of exponents, the given expression, $
5^{1/4}\cdot5^{1/8}
,$ simplifies to
\begin{array}{l}\require{cancel}
5^{\frac{1}{4}+\frac{1}{8}}
\\\\=
5^{\frac{2}{8}+\frac{1}{8}}
\\\\=
5^{\frac{3}{8}}
\\\\=
5^{3/8}
.\end{array}