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\left(9^{\frac{3}{8}}\right)^{-\frac{4}{3}}
Use the rules of exponents to simplify the expression.
9^{\frac{3}{8}\left(-\frac{4}{3}\right)}
To raise a power to another power, multiply the exponents.
9^{-\frac{1}{2}}
Multiply \frac{3}{8} times -\frac{4}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.
\frac{1}{3}
Raise 9 to the power -\frac{1}{2}.