Answer
$\sqrt[5]{y^2}$
Work Step by Step
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 given expression is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{y}}{\sqrt[10]{y}}
\\\\=
\dfrac{y^{1/2}}{y^{1/10}}
.\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{y^{1/2}}{y^{1/10}}
\\\\=
y^{\frac{1}{2}-\frac{1}{10}}
\\\\=
y^{\frac{5}{10}-\frac{1}{10}}
\\\\=
y^{\frac{4}{10}}
\\\\=
y^{\frac{2}{5}}
.\end{array}
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 given expression is equivalent to
\begin{array}{l}\require{cancel}
y^{\frac{2}{5}}
\\\\=
\sqrt[5]{y^2}
.\end{array}
