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\frac{1}{64^{-\frac{2}{3}}}
Use the rules of exponents to simplify the expression.
64^{-\frac{2}{3}\left(-1\right)}
To raise a power to another power, multiply the exponents.
64^{\frac{2}{3}}
Multiply -\frac{2}{3} times -1.
16
Raise 64 to the power \frac{2}{3}.