Find the Domain square root of x^13

$\sqrt{x^{13}}$

Step 1

Set the radicand in $\sqrt{x^{13}}$ greater than or equal to $0$ to find where the expression is defined.

$x^{13} \geq 0$

Step 2

Solve for $x$ .

Take the specified root of both sides of the inequality to eliminate the exponent on the left side.

$\sqrt[13]{x^{13}} \geq \sqrt[13]{0}$

Simplify the equation.

Simplify the left side.

Pull terms out from under the radical.

$x \geq \sqrt[13]{0}$

Simplify the right side.

Simplify $\sqrt[13]{0}$ .

Rewrite $0$ as $0^{13}$ .

$x \geq \sqrt[13]{0^{13}}$

Pull terms out from under the radical.

$x \geq 0$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 4