Solve sqrt[5]{(-1/3)^2*(-1/3)^3}

$$\sqrt[ 5 ] { ( \frac { - 1 } { 3 } ) ^ { 2 } \cdot ( \frac { - 1 } { 3 } ) ^ { 3 } }$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\sqrt[5]{\left(\frac{-1}{3}\right)^{5}}$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$\sqrt[5]{\left(-\frac{1}{3}\right)^{5}}$$

Calculate -\frac{1}{3} to the power of 5 and get -\frac{1}{243}.

$$\sqrt[5]{-\frac{1}{243}}$$

Calculate \sqrt[5]{-\frac{1}{243}} and get -\frac{1}{3}.

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

Factor

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