#### Answer

$y^{1/30}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the definition of rational exponents and the laws of exponents to simplify the given expression, $
\sqrt[3]{\sqrt[5]{\sqrt[]{y}}}
.$
$\bf{\text{Solution Details:}}$
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}
\sqrt[3]{\sqrt[5]{\sqrt[2]{y}}}
\\\\=
\sqrt[3]{\sqrt[5]{y^{1/2}}}
\\\\=
\sqrt[3]{(y^{1/2})^{1/5}}
\\\\=
((y^{1/2})^{1/5})^{1/3}
.\end{array}
Using the Power Rule of the laws of exponents which is given by $\left( x^m \right)^p=x^{mp},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
y^{\frac{1}{2}\cdot\frac{1}{5}\cdot\frac{1}{3}}
\\\\=
y^{\frac{1}{30}}
\\\\=
y^{1/30}
.\end{array}