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\sqrt[3]{\left(-4\right)^{3}}-\left(-2\right)^{4}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
\sqrt[3]{-64}-\left(-2\right)^{4}
Calculate -4 to the power of 3 and get -64.
-4-\left(-2\right)^{4}
Calculate \sqrt[3]{-64} and get -4.
-4-16
Calculate -2 to the power of 4 and get 16.
-20
Subtract 16 from -4 to get -20.