#### Answer

$\dfrac{1}{10}$

#### Work Step by Step

Using the laws of exponents, the given expression, $
10,000^{-1/4}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{1}{10,000^{1/4}}
.\end{array}
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $
\dfrac{1}{10,000^{1/4}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{1}{\sqrt[4]{10,000^1}}
\\\\=
\dfrac{1}{\sqrt[4]{10,000}}
\\\\=
\dfrac{1}{\sqrt[4]{(10)^4}}
\\\\=
\dfrac{1}{10}
.\end{array}