Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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