Solve 10+sqrt[3]{frac{8/27}}{{left(2/3right)}^2}-4/5{left(5/2right)}^8

$$10+ \frac{ \sqrt[ 3 ]{ \frac{ 8 }{ 27 } } }{ { \left( \frac{ 2 }{ 3 } \right) }^{ 2 } } - \frac{ 4 }{ 5 } { \left( \frac{ 5 }{ 2 } \right) }^{ 8 }$$

Evaluate

$$-\frac{77389}{64}=-1209.203125$$

Solution Steps

Calculate \sqrt[3]{\frac{8}{27}} and get \frac{2}{3}.

$$10+\frac{\frac{2}{3}}{\left(\frac{2}{3}\right)^{2}}-\frac{4}{5}\times \left(\frac{5}{2}\right)^{8}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$10+\frac{\frac{2}{3}}{\frac{4}{9}}-\frac{4}{5}\times \left(\frac{5}{2}\right)^{8}$$

Divide \frac{2}{3} by \frac{4}{9} by multiplying \frac{2}{3} by the reciprocal of \frac{4}{9}.

$$10+\frac{2}{3}\times \frac{9}{4}-\frac{4}{5}\times \left(\frac{5}{2}\right)^{8}$$

Multiply \frac{2}{3} and \frac{9}{4} to get \frac{3}{2}.

$$10+\frac{3}{2}-\frac{4}{5}\times \left(\frac{5}{2}\right)^{8}$$

Add 10 and \frac{3}{2} to get \frac{23}{2}.

$$\frac{23}{2}-\frac{4}{5}\times \left(\frac{5}{2}\right)^{8}$$

Calculate \frac{5}{2} to the power of 8 and get \frac{390625}{256}.

$$\frac{23}{2}-\frac{4}{5}\times \frac{390625}{256}$$

Multiply \frac{4}{5} and \frac{390625}{256} to get \frac{78125}{64}.

$$\frac{23}{2}-\frac{78125}{64}$$

Subtract \frac{78125}{64} from \frac{23}{2} to get -\frac{77389}{64}.

$$-\frac{77389}{64}$$

Factor

$$-\frac{77389}{64} = -1209\frac{13}{64} = -1209.203125$$