Finite Math Examples

$\sqrt{49 x^{11}}$

Step 1

Set the radicand in $\sqrt{49 x^{11}}$ less than $0$ to find where the expression is undefined.

$49 x^{11} < 0$

Step 2

Solve for $x$ .

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Step 2.1

Divide each term in $49 x^{11} < 0$ by $49$ and simplify.

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Step 2.1.1

Divide each term in $49 x^{11} < 0$ by $49$ .

$\frac{49 x^{11}}{49} < \frac{0}{49}$

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.

$\frac{49 x^{11}}{49} < \frac{0}{49}$

Step 2.1.2.1.2

Divide $x^{11}$ by $1$ .

$x^{11} < \frac{0}{49}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Divide $0$ by $49$ .

$x^{11} < 0$

Step 2.2

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

$\sqrt[11]{x^{11}} < \sqrt[11]{0}$

Step 2.3

Simplify the equation.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Pull terms out from under the radical.

$x < \sqrt[11]{0}$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Simplify $\sqrt[11]{0}$ .

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Step 2.3.2.1.1

Rewrite $0$ as $0^{11}$ .

$x < \sqrt[11]{0^{11}}$

Step 2.3.2.1.2

Pull terms out from under the radical.

$x < 0$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x < 0$

$(- \infty, 0)$

Step 4