Solve (-2/5)^-2-(0.4)^-2-2^-3+(3/5)^-1

$$( - \frac { 2 } { 5 } ) ^ { - 2 } - ( 0.4 ) ^ { - 2 } - 2 ^ { - 3 } + ( \frac { 3 } { 5 } ) ^ { - 1 }$$

Evaluate

$$\frac{37}{24}\approx 1.541666667$$

Solution Steps

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

$$\frac{25}{4}-0.4^{-2}-2^{-3}+\left(\frac{3}{5}\right)^{-1}$$

Calculate 0.4 to the power of -2 and get 6.25.

$$\frac{25}{4}-6.25-2^{-3}+\left(\frac{3}{5}\right)^{-1}$$

Subtract 6.25 from \frac{25}{4} to get 0.

$$0-2^{-3}+\left(\frac{3}{5}\right)^{-1}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$0-\frac{1}{8}+\left(\frac{3}{5}\right)^{-1}$$

Subtract \frac{1}{8} from 0 to get -\frac{1}{8}.

$$-\frac{1}{8}+\left(\frac{3}{5}\right)^{-1}$$

Calculate \frac{3}{5} to the power of -1 and get \frac{5}{3}.

$$-\frac{1}{8}+\frac{5}{3}$$

Add -\frac{1}{8} and \frac{5}{3} to get \frac{37}{24}.

$$\frac{37}{24}$$

Factor

$$\frac{37}{3 \cdot 2 ^ {3}} = 1\frac{13}{24} = 1.5416666666666667$$