Solve frac{4^frac{3{2}}}{sqrt{25^3}}divsqrt[3]{1/125}

$$\frac { 4 ^ { \frac { 3 } { 2 } } } { \sqrt { 25 ^ { 3 } } } \div \sqrt[ 3 ] { \frac { 1 } { 125 } }$$

Evaluate

$$\frac{8}{25}=0.32$$

Solution Steps

Express \frac{\frac{4^{\frac{3}{2}}}{\sqrt{25^{3}}}}{\sqrt[3]{\frac{1}{125}}} as a single fraction.

$$\frac{4^{\frac{3}{2}}}{\sqrt{25^{3}}\sqrt[3]{\frac{1}{125}}}$$

Calculate 4 to the power of \frac{3}{2} and get 8.

$$\frac{8}{\sqrt{25^{3}}\sqrt[3]{\frac{1}{125}}}$$

Calculate 25 to the power of 3 and get 15625.

$$\frac{8}{\sqrt{15625}\sqrt[3]{\frac{1}{125}}}$$

Calculate the square root of 15625 and get 125.

$$\frac{8}{125\sqrt[3]{\frac{1}{125}}}$$

Calculate \sqrt[3]{\frac{1}{125}} and get \frac{1}{5}.

$$\frac{8}{125\times \frac{1}{5}}$$

Multiply 125 and \frac{1}{5} to get 25.

$$\frac{8}{25}$$

Factor

$$\frac{2 ^ {3}}{5 ^ {2}} = 0.32$$