Linear Algebra Examples

$\sqrt{49 w^{16}}$

Step 1

Set the radicand in $\sqrt{49 w^{16}}$ greater than or equal to $0$ to find where the expression is defined.

$49 w^{16} \geq 0$

Step 2

Solve for $w$ .

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Step 2.1

Divide each term in $49 w^{16} \geq 0$ by $49$ and simplify.

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Step 2.1.1

Divide each term in $49 w^{16} \geq 0$ by $49$ .

$\frac{49 w^{16}}{49} \geq \frac{0}{49}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $49$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{49 w^{16}}{49} \geq \frac{0}{49}$

Step 2.1.2.1.2

Divide $w^{16}$ by $1$ .

$w^{16} \geq \frac{0}{49}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Divide $0$ by $49$ .

$w^{16} \geq 0$

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:

${w | w \in ℝ}$

Step 4