Answer
$\sqrt[8]{t}$
Work Step by Step
Using $x^{m/n}=\sqrt[n]{x^m}=\left(\sqrt[n]{x} \right)^m,$ then
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{t}}{\sqrt[8]{t^3}}
\\\\=
\dfrac{t^{1/2}}{t^{3/8}}
.\end{array}
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
\dfrac{t^{1/2}}{t^{3/8}}
\\\\=
t^{\frac{1}{2}-\frac{3}{8}}
\\\\=
t^{\frac{4}{8}-\frac{3}{8}}
\\\\=
t^{\frac{1}{8}}
.\end{array}
Using $x^{m/n}=\sqrt[n]{x^m}=\left(\sqrt[n]{x} \right)^m,$ then
\begin{array}{l}\require{cancel}
t^{\frac{1}{8}}
\\\\=
\sqrt[8]{t^1}
\\\\=
\sqrt[8]{t}
.\end{array}
