Solve (4*10/5*8)^3*(15*8^2/2*10^2)^2=

$$( \frac { 4 * 10 } { 5 * 8 } ) ^ { 3 } * ( \frac { 15 * 8 ^ { 2 } } { 2 * 10 ^ { 2 } } ) ^ { 2 } =$$

Evaluate

$$\frac{576}{25}=23.04$$

Solution Steps

Cancel out 2\times 4\times 5 in both numerator and denominator.

$$1^{3}\times \left(\frac{15\times 8^{2}}{2\times 10^{2}}\right)^{2}$$

Calculate 1 to the power of 3 and get 1.

$$1\times \left(\frac{15\times 8^{2}}{2\times 10^{2}}\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$1\times \left(\frac{15\times 64}{2\times 10^{2}}\right)^{2}$$

Multiply 15 and 64 to get 960.

$$1\times \left(\frac{960}{2\times 10^{2}}\right)^{2}$$

Calculate 10 to the power of 2 and get 100.

$$1\times \left(\frac{960}{2\times 100}\right)^{2}$$

Multiply 2 and 100 to get 200.

$$1\times \left(\frac{960}{200}\right)^{2}$$

Reduce the fraction \frac{960}{200} to lowest terms by extracting and canceling out 40.

$$1\times \left(\frac{24}{5}\right)^{2}$$

Calculate \frac{24}{5} to the power of 2 and get \frac{576}{25}.

$$1\times \frac{576}{25}$$

Multiply 1 and \frac{576}{25} to get \frac{576}{25}.

$$\frac{576}{25}$$

Factor

$$\frac{2 ^ {6} \cdot 3 ^ {2}}{5 ^ {2}} = 23\frac{1}{25} = 23.04$$