Solve 10div4*6/[frac{2{5}(sqrt[3]{27}-|-9|+2^2)^2]}

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

Evaluate

$$\frac{75}{8}=9.375$$

Solution Steps

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

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

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

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

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

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

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -9 is 9.

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

Subtract 9 from 3 to get -6.

$$\frac{15}{\frac{2}{5}\left(-6+2^{2}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{15}{\frac{2}{5}\left(-6+4\right)^{2}}$$

Add -6 and 4 to get -2.

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

Calculate -2 to the power of 2 and get 4.

$$\frac{15}{\frac{2}{5}\times 4}$$

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

$$\frac{15}{\frac{8}{5}}$$

Divide 15 by \frac{8}{5} by multiplying 15 by the reciprocal of \frac{8}{5}.

$$15\times \frac{5}{8}$$

Multiply 15 and \frac{5}{8} to get \frac{75}{8}.

$$\frac{75}{8}$$

Factor

$$\frac{3 \cdot 5 ^ {2}}{2 ^ {3}} = 9\frac{3}{8} = 9.375$$