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\left(\sqrt[3]{\frac{1}{27}}\right)^{4}
Use the rules of exponents to simplify the expression.
\left(\frac{1}{27}\right)^{\frac{1}{3}\times 4}
To raise a power to another power, multiply the exponents.
\left(\frac{1}{27}\right)^{\frac{4}{3}}
Multiply \frac{1}{3} times 4.
\frac{1}{81}
Raise \frac{1}{27} to the power \frac{4}{3}.