Solve (1-3/2)^-4+(1+1/5)^2

$$( 1 - \frac { 3 } { 2 } ) ^ { - 4 } + ( 1 + \frac { 1 } { 5 } ) ^ { 2 }$$

Evaluate

$$\frac{436}{25}=17.44$$

Solution Steps

Subtract \frac{3}{2} from 1 to get -\frac{1}{2}.

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

Calculate -\frac{1}{2} to the power of -4 and get 16.

$$16+\left(1+\frac{1}{5}\right)^{2}$$

Add 1 and \frac{1}{5} to get \frac{6}{5}.

$$16+\left(\frac{6}{5}\right)^{2}$$

Calculate \frac{6}{5} to the power of 2 and get \frac{36}{25}.

$$16+\frac{36}{25}$$

Add 16 and \frac{36}{25} to get \frac{436}{25}.

$$\frac{436}{25}$$

Factor

$$\frac{2 ^ {2} \cdot 109}{5 ^ {2}} = 17\frac{11}{25} = 17.44$$