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\frac{1}{\left(\frac{3}{2}\right)^{3}}
Use the rules of exponents to simplify the expression.
\left(\frac{3}{2}\right)^{3\left(-1\right)}
To raise a power to another power, multiply the exponents.
\left(\frac{3}{2}\right)^{-3}
Multiply 3 times -1.
\frac{8}{27}
Raise \frac{3}{2} to the power -3.