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\sqrt[3]{8^{-2}}
Use the rules of exponents to simplify the expression.
8^{-2\times \frac{1}{3}}
To raise a power to another power, multiply the exponents.
8^{-\frac{2}{3}}
Multiply -2 times \frac{1}{3}.
\frac{1}{4}
Raise 8 to the power -\frac{2}{3}.