Answer
$x^{-1/4}=\dfrac{1}{\sqrt[4]{x}}$
Work Step by Step
Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the given expression, $
x^{-7}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{1}{x^7}
.\end{array}
In the same manner, the other given expression, $
x^{-1/4}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{1}{x^{1/4}}
.\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 expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{1}{\sqrt[4]{x^1}}
\\=
\dfrac{1}{\sqrt[4]{x}}
.\end{array}
