Solve (4^2/5)*(4^-3/5)+(2^2/5^2)

$$( \frac{ { 4 }^{ 2 } }{ 5 } ) \times ( \frac{ { 4 }^{ -3 } }{ 5 } )+( \frac{ { 2 }^{ 2 } }{ { 5 }^{ 2 } } )$$

Evaluate

$$\frac{17}{100}=0.17$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{16}{5}\times \frac{4^{-3}}{5}+\frac{2^{2}}{5^{2}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{16}{5}\times \frac{\frac{1}{64}}{5}+\frac{2^{2}}{5^{2}}$$

Express \frac{\frac{1}{64}}{5} as a single fraction.

$$\frac{16}{5}\times \frac{1}{64\times 5}+\frac{2^{2}}{5^{2}}$$

Multiply 64 and 5 to get 320.

$$\frac{16}{5}\times \frac{1}{320}+\frac{2^{2}}{5^{2}}$$

Multiply \frac{16}{5} and \frac{1}{320} to get \frac{1}{100}.

$$\frac{1}{100}+\frac{2^{2}}{5^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{100}+\frac{4}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{1}{100}+\frac{4}{25}$$

Add \frac{1}{100} and \frac{4}{25} to get \frac{17}{100}.

$$\frac{17}{100}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 5 ^ {2}} = 0.17$$