Finite Math Examples

$\frac{\sqrt[3]{x^{3}}}{\sqrt[5]{x^{2}}}$

Step 1

Set the denominator in $\frac{\sqrt[3]{x^{3}}}{\sqrt[5]{x^{2}}}$ equal to $0$ to find where the expression is undefined.

$\sqrt[5]{x^{2}} = 0$

Step 2

Solve for $x$ .

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Step 2.1

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $5$ .

${\sqrt[5]{x^{2}}}^{5} = 0^{5}$

Step 2.2

Simplify each side of the equation.

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Step 2.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{x^{2}}$ as $x^{\frac{2}{5}}$ .

${(x^{\frac{2}{5}})}^{5} = 0^{5}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Multiply the exponents in ${(x^{\frac{2}{5}})}^{5}$ .

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Step 2.2.2.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{2}{5} \cdot 5} = 0^{5}$

Step 2.2.2.1.2

Cancel the common factor of $5$ .

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Step 2.2.2.1.2.1

Cancel the common factor.

$x^{\frac{2}{5} \cdot 5} = 0^{5}$

Step 2.2.2.1.2.2

Rewrite the expression.

$x^{2} = 0^{5}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Raising $0$ to any positive power yields $0$ .

$x^{2} = 0$

Step 2.3

Solve for $x$ .

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Step 2.3.1

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

$x = \pm \sqrt{0}$

Step 2.3.2

Simplify $\pm \sqrt{0}$ .

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Step 2.3.2.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 2.3.2.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Step 2.3.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 3