Solve 10/46/2{5/left(sqrt[3]{27--9+2^2right)}^2}

$$\frac{ \frac{ 10 }{ 4 } 6 }{ \frac{ 2 }{ 5 } { \left( \sqrt[ 3 ]{ 27 } --9+ { 2 }^{ 2 } \right) }^{ 2 } }$$

Evaluate

$$\frac{75}{512}=0.146484375$$

Solution Steps

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{5}{2}\times 6}{\frac{2}{5}\left(\sqrt[3]{27}-\left(-9\right)+2^{2}\right)^{2}}$$

Multiply \frac{5}{2} and 6 to get 15.

$$\frac{15}{\frac{2}{5}\left(\sqrt[3]{27}-\left(-9\right)+2^{2}\right)^{2}}$$

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

$$\frac{15}{\frac{2}{5}\left(3-\left(-9\right)+2^{2}\right)^{2}}$$

The opposite of -9 is 9.

$$\frac{15}{\frac{2}{5}\left(3+9+2^{2}\right)^{2}}$$

Add 3 and 9 to get 12.

$$\frac{15}{\frac{2}{5}\left(12+2^{2}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{15}{\frac{2}{5}\left(12+4\right)^{2}}$$

Add 12 and 4 to get 16.

$$\frac{15}{\frac{2}{5}\times 16^{2}}$$

Calculate 16 to the power of 2 and get 256.

$$\frac{15}{\frac{2}{5}\times 256}$$

Multiply \frac{2}{5} and 256 to get \frac{512}{5}.

$$\frac{15}{\frac{512}{5}}$$

Divide 15 by \frac{512}{5} by multiplying 15 by the reciprocal of \frac{512}{5}.

$$15\times \frac{5}{512}$$

Multiply 15 and \frac{5}{512} to get \frac{75}{512}.

$$\frac{75}{512}$$

Factor

$$\frac{3 \cdot 5 ^ {2}}{2 ^ {9}} = 0.146484375$$