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\sqrt[3]{\left(-\frac{1}{2}\right)^{6}}
Use the rules of exponents to simplify the expression.
\left(-\frac{1}{2}\right)^{6\times \frac{1}{3}}
To raise a power to another power, multiply the exponents.
\left(-\frac{1}{2}\right)^{2}
Multiply 6 times \frac{1}{3}.
\frac{1}{4}
Raise -\frac{1}{2} to the power 2.