Solve for x x^x = ninth root of 1/3

$x^{x} = \sqrt[9]{\frac{1}{3}}$

Step 1

Simplify $\sqrt[9]{\frac{1}{3}}$ .

Rewrite $\sqrt[9]{\frac{1}{3}}$ as $\frac{\sqrt[9]{1}}{\sqrt[9]{3}}$ .

$x^{x} = \frac{\sqrt[9]{1}}{\sqrt[9]{3}}$

Any root of $1$ is $1$ .

$x^{x} = \frac{1}{\sqrt[9]{3}}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 0.03703703, 0.86894198$

Step 3