Solve (1/5)^2(1-1/5)^4-2

$$( \frac { 1 } { 5 } ) ^ { 2 } ( 1 - \frac { 1 } { 5 } ) ^ { 4 - 2 }$$

Evaluate

$$\frac{16}{625}=0.0256$$

Solution Steps

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$\frac{1}{25}\left(1-\frac{1}{5}\right)^{4-2}$$

Subtract \frac{1}{5} from 1 to get \frac{4}{5}.

$$\frac{1}{25}\times \left(\frac{4}{5}\right)^{4-2}$$

Subtract 2 from 4 to get 2.

$$\frac{1}{25}\times \left(\frac{4}{5}\right)^{2}$$

Calculate \frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$\frac{1}{25}\times \frac{16}{25}$$

Multiply \frac{1}{25} and \frac{16}{25} to get \frac{16}{625}.

$$\frac{16}{625}$$

Factor

$$\frac{2 ^ {4}}{5 ^ {4}} = 0.0256$$