Answer
$\dfrac{1}{10}$
Work Step by Step
Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ then
\begin{array}{l}\require{cancel}
100^{-1/2}
\\\\=
\dfrac{1}{100^{1/2}}
.\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}{100^{1/2}}
\\\\=
\dfrac{1}{\sqrt{100^1}}
\\\\=
\dfrac{1}{\sqrt{100}}
\\\\=
\dfrac{1}{\sqrt{(10)^2}}
\\\\=
\dfrac{1}{10}
.\end{array}
