Finite Math Examples

$\frac{10 z^{4}}{11 r^{3}} \cdot \frac{121 r^{5}}{100 z}$

Step 1

Set the denominator in $\frac{10 z^{4}}{11 r^{3}}$ equal to $0$ to find where the expression is undefined.

$11 r^{3} = 0$

Step 2

Solve for $z$ .

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Step 2.1

Divide each term in $11 r^{3} = 0$ by $11$ and simplify.

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Step 2.1.1

Divide each term in $11 r^{3} = 0$ by $11$ .

$\frac{11 r^{3}}{11} = \frac{0}{11}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $11$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{11 r^{3}}{11} = \frac{0}{11}$

Step 2.1.2.1.2

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

$r^{3} = \frac{0}{11}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Divide $0$ by $11$ .

$r^{3} = 0$

Step 2.2

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

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

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

$r = 0$

Step 3

Set the denominator in $\frac{121 r^{5}}{100 z}$ equal to $0$ to find where the expression is undefined.

$100 z = 0$

Step 4

Divide each term in $100 z = 0$ by $100$ and simplify.

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Step 4.1

Divide each term in $100 z = 0$ by $100$ .

$\frac{100 z}{100} = \frac{0}{100}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $100$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{100 z}{100} = \frac{0}{100}$

Step 4.2.1.2

Divide $z$ by $1$ .

$z = \frac{0}{100}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $100$ .

$z = 0$

Step 5

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

Interval Notation:

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

Set-Builder Notation:

${z | z \neq 0}$