Solve sqrt[3]{-64/125}-sqrt[3]{8}+sqrt{1/100}--2^3sqrt[3]{0.064}

$$\sqrt[ 3 ]{ - \frac{ 64 }{ 125 } } - \sqrt[ 3 ]{ 8 } + \sqrt{ \frac{ 1 }{ 100 } } - { -2 }^{ 3 } \sqrt[ 3 ]{ 0.064 }$$

Evaluate

$$0.5$$

Solution Steps

Calculate \sqrt[3]{-\frac{64}{125}} and get -\frac{4}{5}.

$$-\frac{4}{5}-\sqrt[3]{8}+\sqrt{\frac{1}{100}}-\left(-2\right)^{3}\sqrt[3]{0.064}$$

Calculate \sqrt[3]{8} and get 2.

$$-\frac{4}{5}-2+\sqrt{\frac{1}{100}}-\left(-2\right)^{3}\sqrt[3]{0.064}$$

Subtract 2 from -\frac{4}{5} to get -\frac{14}{5}.

$$-\frac{14}{5}+\sqrt{\frac{1}{100}}-\left(-2\right)^{3}\sqrt[3]{0.064}$$

Rewrite the square root of the division \frac{1}{100} as the division of square roots \frac{\sqrt{1}}{\sqrt{100}}. Take the square root of both numerator and denominator.

$$-\frac{14}{5}+\frac{1}{10}-\left(-2\right)^{3}\sqrt[3]{0.064}$$

Add -\frac{14}{5} and \frac{1}{10} to get -\frac{27}{10}.

$$-\frac{27}{10}-\left(-2\right)^{3}\sqrt[3]{0.064}$$

Calculate -2 to the power of 3 and get -8.

$$-\frac{27}{10}-\left(-8\sqrt[3]{0.064}\right)$$

Calculate \sqrt[3]{0.064} and get \frac{2}{5}.

$$-\frac{27}{10}-\left(-8\times \frac{2}{5}\right)$$

Multiply -8 and \frac{2}{5} to get -\frac{16}{5}.

$$-\frac{27}{10}-\left(-\frac{16}{5}\right)$$

The opposite of -\frac{16}{5} is \frac{16}{5}.

$$-\frac{27}{10}+\frac{16}{5}$$

Add -\frac{27}{10} and \frac{16}{5} to get \frac{1}{2}.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$