Finite Math Examples

$\frac{4 b}{3 a^{4}} \cdot \frac{a^{5} b}{10 b^{3}}$

Step 1

Set the denominator in $\frac{4 b}{3 a^{4}}$ equal to $0$ to find where the expression is undefined.

$3 a^{4} = 0$

Step 2

Solve for $b$ .

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Step 2.1

Divide each term in $3 a^{4} = 0$ by $3$ and simplify.

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Step 2.1.1

Divide each term in $3 a^{4} = 0$ by $3$ .

$\frac{3 a^{4}}{3} = \frac{0}{3}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $3$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{3 a^{4}}{3} = \frac{0}{3}$

Step 2.1.2.1.2

Divide $a^{4}$ by $1$ .

$a^{4} = \frac{0}{3}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Divide $0$ by $3$ .

$a^{4} = 0$

Step 2.2

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

$a = \pm \sqrt[4]{0}$

Step 2.3

Simplify $\pm \sqrt[4]{0}$ .

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Step 2.3.1

Rewrite $0$ as $0^{4}$ .

$a = \pm \sqrt[4]{0^{4}}$

Step 2.3.2

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

$a = \pm 0$

Step 2.3.3

Plus or minus $0$ is $0$ .

$a = 0$

Step 3

Set the denominator in $\frac{a^{5} b}{10 b^{3}}$ equal to $0$ to find where the expression is undefined.

$10 b^{3} = 0$

Step 4

Solve for $b$ .

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Step 4.1

Divide each term in $10 b^{3} = 0$ by $10$ and simplify.

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Step 4.1.1

Divide each term in $10 b^{3} = 0$ by $10$ .

$\frac{10 b^{3}}{10} = \frac{0}{10}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $10$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{10 b^{3}}{10} = \frac{0}{10}$

Step 4.1.2.1.2

Divide $b^{3}$ by $1$ .

$b^{3} = \frac{0}{10}$

Step 4.1.3

Simplify the right side.

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Step 4.1.3.1

Divide $0$ by $10$ .

$b^{3} = 0$

Step 4.2

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

$b = \sqrt[3]{0}$

Step 4.3

Simplify $\sqrt[3]{0}$ .

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Step 4.3.1

Rewrite $0$ as $0^{3}$ .

$b = \sqrt[3]{0^{3}}$

Step 4.3.2

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

$b = 0$

Step 5

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

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${b | b \neq 0}$