# To calculate the expression -9^{\frac{-3}{2}}.

To calculate the expression $-{9}^{\frac{-3}{2}}$.
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Calculation:
According to the power rule $\left({b}^{n}\right)m={b}^{n}\cdot m$
This can be written as $-{9}^{\frac{-3}{2}}=-{\left(3×3\right)}^{\frac{-3}{2}}$
$-{9}^{\frac{-3}{2}}=-{\left({3}^{2}\right)}^{\frac{-3}{2}}$
Applying the power rule,
$-{9}^{\frac{-3}{2}}=-{\left(3\right)}^{2×\frac{-3}{2}}$
$-{9}^{\frac{-3}{2}}=-{\left(3\right)}^{-3}$
$-{9}^{\frac{-3}{2}}=-{\left(27\right)}^{-1}$
$-{9}^{\frac{-3}{2}}=\frac{-1}{27}$