## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\dfrac{1}{10}$
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}