Solve (1/5)^-1+(1/3)^-2/(frac{1{5})^-2-(1/3)^-1}

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

Evaluate

$$\frac{7}{11}\approx 0.636363636$$

Solution Steps

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

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

Calculate \frac{1}{3} to the power of -2 and get 9.

$$\frac{5+9}{\left(\frac{1}{5}\right)^{-2}-\left(\frac{1}{3}\right)^{-1}}$$

Add 5 and 9 to get 14.

$$\frac{14}{\left(\frac{1}{5}\right)^{-2}-\left(\frac{1}{3}\right)^{-1}}$$

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

$$\frac{14}{25-\left(\frac{1}{3}\right)^{-1}}$$

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

$$\frac{14}{25-3}$$

Subtract 3 from 25 to get 22.

$$\frac{14}{22}$$

Reduce the fraction \frac{14}{22} to lowest terms by extracting and canceling out 2.

$$\frac{7}{11}$$

Factor

$$\frac{7}{11} = 0.6363636363636364$$