Solve (-1/5)^-3-(-1/5)^-2:(-5)^5-(-1/5)^-2

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

Evaluate

$$-\frac{18749}{125}=-149.992$$

Solution Steps

Calculate -\frac{1}{5} to the power of -3 and get -125.

$$-125-\frac{\left(-\frac{1}{5}\right)^{-2}}{\left(-5\right)^{5}}-\left(-\frac{1}{5}\right)^{-2}$$

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

$$-125-\frac{25}{\left(-5\right)^{5}}-\left(-\frac{1}{5}\right)^{-2}$$

Calculate -5 to the power of 5 and get -3125.

$$-125-\frac{25}{-3125}-\left(-\frac{1}{5}\right)^{-2}$$

Reduce the fraction \frac{25}{-3125} to lowest terms by extracting and canceling out 25.

$$-125-\left(-\frac{1}{125}\right)-\left(-\frac{1}{5}\right)^{-2}$$

The opposite of -\frac{1}{125} is \frac{1}{125}.

$$-125+\frac{1}{125}-\left(-\frac{1}{5}\right)^{-2}$$

Add -125 and \frac{1}{125} to get -\frac{15624}{125}.

$$-\frac{15624}{125}-\left(-\frac{1}{5}\right)^{-2}$$

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

$$-\frac{15624}{125}-25$$

Subtract 25 from -\frac{15624}{125} to get -\frac{18749}{125}.

$$-\frac{18749}{125}$$

Factor

$$-\frac{18749}{125} = -149\frac{124}{125} = -149.992$$