#### Answer

$x^{1/16}$

#### 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{\sqrt{\sqrt{\sqrt{x}}}}
.$
$\bf{\text{Solution Details:}}$
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[2]{\sqrt[2]{\sqrt[2]{\sqrt[2]{x}}}}
\\\\=
\sqrt[2]{\sqrt[2]{\sqrt[2]{x^{1/2}}}}
\\\\=
\sqrt[2]{\sqrt[2]{(x^{1/2})^{1/2}}}
\\\\=
\sqrt[2]{((x^{1/2})^{1/2})^{1/2}}
\\\\=
(((x^{1/2})^{1/2})^{1/2})^{1/2}
.\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}
x^{\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}}
\\\\=
x^{\frac{1}{16}}
\\\\=
x^{1/16}
.\end{array}