Solve {left(64/125right)}^frac{2{3}}+1/{left(frac{256{625}right)}^frac{1{4}}}+frac{sqrt{25}}{sqrt[3]{64}}

$${ \left( \frac{ 64 }{ 125 } \right) }^{ \frac{ 2 }{ 3 } } + \frac{ 1 }{ { \left( \frac{ 256 }{ 625 } \right) }^{ \frac{ 1 }{ 4 } } } + \frac{ \sqrt{ 25 } }{ \sqrt[ 3 ]{ 64 } }$$

Evaluate

$$\frac{157}{50}=3.14$$

Solution Steps

Calculate \frac{64}{125} to the power of \frac{2}{3} and get \frac{16}{25}.

$$\frac{16}{25}+\frac{1}{\left(\frac{256}{625}\right)^{\frac{1}{4}}}+\frac{\sqrt{25}}{\sqrt[3]{64}}$$

Calculate \frac{256}{625} to the power of \frac{1}{4} and get \frac{4}{5}.

$$\frac{16}{25}+\frac{1}{\frac{4}{5}}+\frac{\sqrt{25}}{\sqrt[3]{64}}$$

Divide 1 by \frac{4}{5} by multiplying 1 by the reciprocal of \frac{4}{5}.

$$\frac{16}{25}+1\times \frac{5}{4}+\frac{\sqrt{25}}{\sqrt[3]{64}}$$

Multiply 1 and \frac{5}{4} to get \frac{5}{4}.

$$\frac{16}{25}+\frac{5}{4}+\frac{\sqrt{25}}{\sqrt[3]{64}}$$

Add \frac{16}{25} and \frac{5}{4} to get \frac{189}{100}.

$$\frac{189}{100}+\frac{\sqrt{25}}{\sqrt[3]{64}}$$

Calculate the square root of 25 and get 5.

$$\frac{189}{100}+\frac{5}{\sqrt[3]{64}}$$

Calculate \sqrt[3]{64} and get 4.

$$\frac{189}{100}+\frac{5}{4}$$

Add \frac{189}{100} and \frac{5}{4} to get \frac{157}{50}.

$$\frac{157}{50}$$

Factor

$$\frac{157}{2 \cdot 5 ^ {2}} = 3\frac{7}{50} = 3.14$$