Answer
$\displaystyle \frac{1000}{1331}$
Work Step by Step
$[\displaystyle \frac{121}{100}]^{-3/2}=$ ... recognize: 121$=11^{2}, $100$=10^{2}$
$=[\displaystyle \frac{11^{2}}{10^{2}}]^{-3/2}=$ ...use: $(\displaystyle \frac{a}{b})^{m}=\frac{a^{m}}{b^{m}}$
$=[(\displaystyle \frac{11}{10})^{2}]^{-3/2}=$ ...use: $(a^{m})^{n}=a^{mn}$
$=(\displaystyle \frac{11}{10})^{-3}=$ ...use: $\displaystyle \frac{1}{a^{n}}=a^{-n}$
$=(\displaystyle \frac{10}{11})^{3}=$ ...use: $(\displaystyle \frac{a}{b})^{m}=\frac{a^{m}}{b^{m}}$
$=\displaystyle \frac{10^{3}}{11^{3}}= \frac{1000}{1331}$
