Answer
$\dfrac{1}{10^{14}}$
Work Step by Step
Use the rule $\dfrac{a^m}{a^n} = a^{m-n}, a\ne0$ to obtain:
$=100^{\frac{3}{4}-\frac{31}{4}}
\\=100^{-\frac{28}{4}}
\\=100^{-7}$
Write 100 as $10^2$ to obtain:
$=(10^2)^{-7}$
Use the rule $(a^m)^n=a^{mn}$ to tobtain:
$=10^{-14}$
Use the rule $a^{-m} = \dfrac{1}{a^m}$ to obtain:
$=\dfrac{1}{10^{14}}$
