Finite Math Examples

$C = 200 \sqrt[3]{n + 200}$

Step 1

Rewrite the equation as $200 \sqrt[3]{n + 200} = C$ .

$200 \sqrt[3]{n + 200} = C$

Step 2

Divide each term in $200 \sqrt[3]{n + 200} = C$ by $200$ and simplify.

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Step 2.1

Divide each term in $200 \sqrt[3]{n + 200} = C$ by $200$ .

$\frac{200 \sqrt[3]{n + 200}}{200} = \frac{C}{200}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $200$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{200 \sqrt[3]{n + 200}}{200} = \frac{C}{200}$

Step 2.2.1.2

Divide $\sqrt[3]{n + 200}$ by $1$ .

$\sqrt[3]{n + 200} = \frac{C}{200}$

Step 3

To remove the radical on the left side of the equation, cube both sides of the equation.

${\sqrt[3]{n + 200}}^{3} = {(\frac{C}{200})}^{3}$

Step 4

Simplify each side of the equation.

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{n + 200}$ as ${(n + 200)}^{\frac{1}{3}}$ .

${({(n + 200)}^{\frac{1}{3}})}^{3} = {(\frac{C}{200})}^{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify ${({(n + 200)}^{\frac{1}{3}})}^{3}$ .

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Step 4.2.1.1

Multiply the exponents in ${({(n + 200)}^{\frac{1}{3}})}^{3}$ .

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Step 4.2.1.1.1

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

${(n + 200)}^{\frac{1}{3} \cdot 3} = {(\frac{C}{200})}^{3}$

Step 4.2.1.1.2

Cancel the common factor of $3$ .

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Step 4.2.1.1.2.1

Cancel the common factor.

${(n + 200)}^{\frac{1}{3} \cdot 3} = {(\frac{C}{200})}^{3}$

Step 4.2.1.1.2.2

Rewrite the expression.

${(n + 200)}^{1} = {(\frac{C}{200})}^{3}$

Step 4.2.1.2

Simplify.

$n + 200 = {(\frac{C}{200})}^{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify ${(\frac{C}{200})}^{3}$ .

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Step 4.3.1.1

Apply the product rule to $\frac{C}{200}$ .

$n + 200 = \frac{C^{3}}{200^{3}}$

Step 4.3.1.2

Raise $200$ to the power of $3$ .

$n + 200 = \frac{C^{3}}{8000000}$

Step 5

Subtract $200$ from both sides of the equation.

$n = \frac{C^{3}}{8000000} - 200$