Solve (3^-1-9^-1/6)^1/3

$$( \frac { 3 ^ { - 1 } - 9 ^ { - 1 } } { 6 } ) ^ { 1 / 3 }$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

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

$$\left(\frac{\frac{1}{3}-9^{-1}}{6}\right)^{\frac{1}{3}}$$

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

$$\left(\frac{\frac{1}{3}-\frac{1}{9}}{6}\right)^{\frac{1}{3}}$$

Subtract \frac{1}{9} from \frac{1}{3} to get \frac{2}{9}.

$$\left(\frac{\frac{2}{9}}{6}\right)^{\frac{1}{3}}$$

Express \frac{\frac{2}{9}}{6} as a single fraction.

$$\left(\frac{2}{9\times 6}\right)^{\frac{1}{3}}$$

Multiply 9 and 6 to get 54.

$$\left(\frac{2}{54}\right)^{\frac{1}{3}}$$

Reduce the fraction \frac{2}{54} to lowest terms by extracting and canceling out 2.

$$\left(\frac{1}{27}\right)^{\frac{1}{3}}$$

Calculate \frac{1}{27} to the power of \frac{1}{3} and get \frac{1}{3}.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$