Solve 1/(-5)-5/(-5)^2-25/(-5)^3-125/(-5)^4

$$\frac { 1 } { ( - 5 ) } - \frac { 5 } { ( - 5 ) ^ { 2 } } - \frac { 25 } { ( - 5 ) ^ { 3 } } - \frac { 125 } { ( - 5 ) ^ { 4 } }$$

Evaluate

$$-\frac{2}{5}=-0.4$$

Solution Steps

Fraction \frac{1}{-5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$-\frac{1}{5}-\frac{5}{\left(-5\right)^{2}}-\frac{25}{\left(-5\right)^{3}}-\frac{125}{\left(-5\right)^{4}}$$

Calculate -5 to the power of 2 and get 25.

$$-\frac{1}{5}-\frac{5}{25}-\frac{25}{\left(-5\right)^{3}}-\frac{125}{\left(-5\right)^{4}}$$

Reduce the fraction \frac{5}{25} to lowest terms by extracting and canceling out 5.

$$-\frac{1}{5}-\frac{1}{5}-\frac{25}{\left(-5\right)^{3}}-\frac{125}{\left(-5\right)^{4}}$$

Since -\frac{1}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-1}{5}-\frac{25}{\left(-5\right)^{3}}-\frac{125}{\left(-5\right)^{4}}$$

Subtract 1 from -1 to get -2.

$$-\frac{2}{5}-\frac{25}{\left(-5\right)^{3}}-\frac{125}{\left(-5\right)^{4}}$$

Calculate -5 to the power of 3 and get -125.

$$-\frac{2}{5}-\frac{25}{-125}-\frac{125}{\left(-5\right)^{4}}$$

Reduce the fraction \frac{25}{-125} to lowest terms by extracting and canceling out 25.

$$-\frac{2}{5}-\left(-\frac{1}{5}\right)-\frac{125}{\left(-5\right)^{4}}$$

The opposite of -\frac{1}{5} is \frac{1}{5}.

$$-\frac{2}{5}+\frac{1}{5}-\frac{125}{\left(-5\right)^{4}}$$

Since -\frac{2}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\frac{-2+1}{5}-\frac{125}{\left(-5\right)^{4}}$$

Add -2 and 1 to get -1.

$$-\frac{1}{5}-\frac{125}{\left(-5\right)^{4}}$$

Calculate -5 to the power of 4 and get 625.

$$-\frac{1}{5}-\frac{125}{625}$$

Reduce the fraction \frac{125}{625} to lowest terms by extracting and canceling out 125.

$$-\frac{1}{5}-\frac{1}{5}$$

Since -\frac{1}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-1}{5}$$

Subtract 1 from -1 to get -2.

$$-\frac{2}{5}$$

Factor

$$-\frac{2}{5} = -0.4$$