Finite Math Examples

$\sqrt[4]{16 x^{12}}$

Step 1

Set the radicand in $\sqrt[4]{16 x^{12}}$ greater than or equal to $0$ to find where the expression is defined.

$16 x^{12} \geq 0$

Step 2

Solve for $x$ .

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Step 2.1

Divide each term in $16 x^{12} \geq 0$ by $16$ and simplify.

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Step 2.1.1

Divide each term in $16 x^{12} \geq 0$ by $16$ .

$\frac{16 x^{12}}{16} \geq \frac{0}{16}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $16$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{16 x^{12}}{16} \geq \frac{0}{16}$

Step 2.1.2.1.2

Divide $x^{12}$ by $1$ .

$x^{12} \geq \frac{0}{16}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Divide $0$ by $16$ .

$x^{12} \geq 0$

Step 2.2

Since the left side has an even power, it is always positive for all real numbers.

All real numbers

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4