Answer
$a]$ $\frac{1}{1000}$
$b]$ $\frac{2}{3}$
Work Step by Step
$a]$ $100^{\frac{-3}{2}}=$ $(10^{2})^\frac{-3}{2}=$ $10^{-3}=$ $\frac{1}{1000}$
$b]$ $(\frac{9}{4})^{\frac{-1}{2}}=$ $(\frac{3}{2})^\frac{2\times-1}{2}= $ $(\frac{3}{2})^{-1}=$ $\frac{2}{3}$