Solve frac{{125}^frac{2{3}}}{{100}^frac{1{2}}*{32}^frac{2{5}}}

$$\frac{ { 125 }^{ \frac{ 2 }{ 3 } } }{ { 100 }^{ \frac{ 1 }{ 2 } } \times { 32 }^{ \frac{ 2 }{ 5 } } }$$

Evaluate

$$\frac{5}{8}=0.625$$

Solution Steps

Calculate 125 to the power of \frac{2}{3} and get 25.

$$\frac{25}{100^{\frac{1}{2}}\times 32^{\frac{2}{5}}}$$

Calculate 100 to the power of \frac{1}{2} and get 10.

$$\frac{25}{10\times 32^{\frac{2}{5}}}$$

Calculate 32 to the power of \frac{2}{5} and get 4.

$$\frac{25}{10\times 4}$$

Multiply 10 and 4 to get 40.

$$\frac{25}{40}$$

Reduce the fraction \frac{25}{40} to lowest terms by extracting and canceling out 5.

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

Factor

$$\frac{5}{2 ^ {3}} = 0.625$$