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\left(\sqrt[4]{16}\right)^{-3}
Use the rules of exponents to simplify the expression.
16^{\frac{1}{4}\left(-3\right)}
To raise a power to another power, multiply the exponents.
16^{-\frac{3}{4}}
Multiply \frac{1}{4} times -3.
\frac{1}{8}
Raise 16 to the power -\frac{3}{4}.