Solve 0.008^frac{1{3}}+sqrt[3]{[(-2)^3]^4}-16^0.75

$$0.008 ^ { \frac { 1 } { 3 } } + \sqrt[ 3 ] { [ ( - 2 ) ^ { 3 } ] ^ { 4 } } - 16 ^ { 0.75 }$$

Evaluate

$$8.2$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$0.008^{\frac{1}{3}}+\sqrt[3]{\left(-2\right)^{12}}-16^{0.75}$$

Calculate 0.008 to the power of \frac{1}{3} and get \frac{1}{5}.

$$\frac{1}{5}+\sqrt[3]{\left(-2\right)^{12}}-16^{0.75}$$

Calculate -2 to the power of 12 and get 4096.

$$\frac{1}{5}+\sqrt[3]{4096}-16^{0.75}$$

Calculate \sqrt[3]{4096} and get 16.

$$\frac{1}{5}+16-16^{0.75}$$

Add \frac{1}{5} and 16 to get \frac{81}{5}.

$$\frac{81}{5}-16^{0.75}$$

Calculate 16 to the power of 0.75 and get 8.

$$\frac{81}{5}-8$$

Subtract 8 from \frac{81}{5} to get \frac{41}{5}.

$$\frac{41}{5}$$

Factor

$$\frac{41}{5} = 8\frac{1}{5} = 8.2$$