Solve (-4/7)^2-(-2/5)^3/-sqrt{frac{64{625}}divsqrt[3]{-8/125}}

$$\frac { ( - \frac { 4 } { 7 } ) ^ { 2 } - ( - \frac { 2 } { 5 } ) ^ { 3 } } { - \sqrt { \frac { 64 } { 625 } } \div \sqrt[ 3 ] { - \frac { 8 } { 125 } } }$$

Evaluate

$$\frac{598}{1225}\approx 0.488163265$$

Solution Steps

Calculate -\frac{4}{7} to the power of 2 and get \frac{16}{49}.

$$\frac{\frac{16}{49}-\left(-\frac{2}{5}\right)^{3}}{\frac{-\sqrt{\frac{64}{625}}}{\sqrt[3]{-\frac{8}{125}}}}$$

Calculate -\frac{2}{5} to the power of 3 and get -\frac{8}{125}.

$$\frac{\frac{16}{49}-\left(-\frac{8}{125}\right)}{\frac{-\sqrt{\frac{64}{625}}}{\sqrt[3]{-\frac{8}{125}}}}$$

The opposite of -\frac{8}{125} is \frac{8}{125}.

$$\frac{\frac{16}{49}+\frac{8}{125}}{\frac{-\sqrt{\frac{64}{625}}}{\sqrt[3]{-\frac{8}{125}}}}$$

Add \frac{16}{49} and \frac{8}{125} to get \frac{2392}{6125}.

$$\frac{\frac{2392}{6125}}{\frac{-\sqrt{\frac{64}{625}}}{\sqrt[3]{-\frac{8}{125}}}}$$

Rewrite the square root of the division \frac{64}{625} as the division of square roots \frac{\sqrt{64}}{\sqrt{625}}. Take the square root of both numerator and denominator.

$$\frac{\frac{2392}{6125}}{\frac{-\frac{8}{25}}{\sqrt[3]{-\frac{8}{125}}}}$$

Calculate \sqrt[3]{-\frac{8}{125}} and get -\frac{2}{5}.

$$\frac{\frac{2392}{6125}}{\frac{-\frac{8}{25}}{-\frac{2}{5}}}$$

Divide -\frac{8}{25} by -\frac{2}{5} by multiplying -\frac{8}{25} by the reciprocal of -\frac{2}{5}.

$$\frac{\frac{2392}{6125}}{-\frac{8}{25}\left(-\frac{5}{2}\right)}$$

Multiply -\frac{8}{25} and -\frac{5}{2} to get \frac{4}{5}.

$$\frac{\frac{2392}{6125}}{\frac{4}{5}}$$

Divide \frac{2392}{6125} by \frac{4}{5} by multiplying \frac{2392}{6125} by the reciprocal of \frac{4}{5}.

$$\frac{2392}{6125}\times \frac{5}{4}$$

Multiply \frac{2392}{6125} and \frac{5}{4} to get \frac{598}{1225}.

$$\frac{598}{1225}$$

Factor

$$\frac{2 \cdot 13 \cdot 23}{5 ^ {2} \cdot 7 ^ {2}} = 0.4881632653061225$$