Solve 10/3[3^-1-(-3)^-1]^-1

$$\frac { 10 } { 3 } [ 3 ^ { - 1 } - ( - 3 ) ^ { - 1 } ] ^ { - 1 }$$

Evaluate

$$5$$

Solution Steps

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

$$\frac{10}{3}\left(\frac{1}{3}-\left(-3\right)^{-1}\right)^{-1}$$

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

$$\frac{10}{3}\left(\frac{1}{3}-\left(-\frac{1}{3}\right)\right)^{-1}$$

The opposite of -\frac{1}{3} is \frac{1}{3}.

$$\frac{10}{3}\left(\frac{1}{3}+\frac{1}{3}\right)^{-1}$$

Add \frac{1}{3} and \frac{1}{3} to get \frac{2}{3}.

$$\frac{10}{3}\times \left(\frac{2}{3}\right)^{-1}$$

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

$$\frac{10}{3}\times \frac{3}{2}$$

Multiply \frac{10}{3} and \frac{3}{2} to get 5.

$$5$$

Factor

$$5$$