Pre-Algebra Examples

$12 x^{3} = \frac{1}{3} \cdot 24$

Step 1

Subtract $\frac{1}{3} \cdot 24$ from both sides of the equation.

$12 x^{3} - \frac{1}{3} \cdot 24 = 0$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$12 x^{3} + \frac{- 1}{3} \cdot 24 = 0$

Step 2.1.2

Factor $3$ out of $24$ .

$12 x^{3} + \frac{- 1}{3} \cdot (3 (8)) = 0$

Step 2.1.3

Cancel the common factor.

$12 x^{3} + \frac{- 1}{3} \cdot (3 \cdot 8) = 0$

Step 2.1.4

Rewrite the expression.

$12 x^{3} - 1 \cdot 8 = 0$

Step 2.2

Multiply $- 1$ by $8$ .

$12 x^{3} - 8 = 0$

Step 3

Factor $4$ out of $12 x^{3} - 8$ .

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Step 3.1

Factor $4$ out of $12 x^{3}$ .

$4 (3 x^{3}) - 8 = 0$

Step 3.2

Factor $4$ out of $- 8$ .

$4 (3 x^{3}) + 4 (- 2) = 0$

Step 3.3

Factor $4$ out of $4 (3 x^{3}) + 4 (- 2)$ .

$4 (3 x^{3} - 2) = 0$

Step 4

Divide each term in $4 (3 x^{3} - 2) = 0$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 (3 x^{3} - 2) = 0$ by $4$ .

$\frac{4 (3 x^{3} - 2)}{4} = \frac{0}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 (3 x^{3} - 2)}{4} = \frac{0}{4}$

Step 4.2.1.2

Divide $3 x^{3} - 2$ by $1$ .

$3 x^{3} - 2 = \frac{0}{4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $4$ .

$3 x^{3} - 2 = 0$

Step 5

Add $2$ to both sides of the equation.

$3 x^{3} = 2$

Step 6

Divide each term in $3 x^{3} = 2$ by $3$ and simplify.

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Step 6.1

Divide each term in $3 x^{3} = 2$ by $3$ .

$\frac{3 x^{3}}{3} = \frac{2}{3}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $3$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{3 x^{3}}{3} = \frac{2}{3}$

Step 6.2.1.2

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

$x^{3} = \frac{2}{3}$

Step 7

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

$x = \sqrt[3]{\frac{2}{3}}$

Step 8

Simplify $\sqrt[3]{\frac{2}{3}}$ .

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Step 8.1

Rewrite $\sqrt[3]{\frac{2}{3}}$ as $\frac{\sqrt[3]{2}}{\sqrt[3]{3}}$ .

$x = \frac{\sqrt[3]{2}}{\sqrt[3]{3}}$

Step 8.2

Multiply $\frac{\sqrt[3]{2}}{\sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

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

Step 8.3

Combine and simplify the denominator.

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Step 8.3.1

Multiply $\frac{\sqrt[3]{2}}{\sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

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

Step 8.3.2

Raise $\sqrt[3]{3}$ to the power of $1$ .

$x = \frac{\sqrt[3]{2} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{1} {\sqrt[3]{3}}^{2}}$

Step 8.3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \frac{\sqrt[3]{2} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{1 + 2}}$

Step 8.3.4

Add $1$ and $2$ .

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

Step 8.3.5

Rewrite ${\sqrt[3]{3}}^{3}$ as $3$ .

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Step 8.3.5.1

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

$x = \frac{\sqrt[3]{2} {\sqrt[3]{3}}^{2}}{{(3^{\frac{1}{3}})}^{3}}$

Step 8.3.5.2

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

$x = \frac{\sqrt[3]{2} {\sqrt[3]{3}}^{2}}{3^{\frac{1}{3} \cdot 3}}$

Step 8.3.5.3

Combine $\frac{1}{3}$ and $3$ .

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

Step 8.3.5.4

Cancel the common factor of $3$ .

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Step 8.3.5.4.1

Cancel the common factor.

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

Step 8.3.5.4.2

Rewrite the expression.

$x = \frac{\sqrt[3]{2} {\sqrt[3]{3}}^{2}}{3^{1}}$

Step 8.3.5.5

Evaluate the exponent.

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

Step 8.4

Simplify the numerator.

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Step 8.4.1

Rewrite ${\sqrt[3]{3}}^{2}$ as $\sqrt[3]{3^{2}}$ .

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

Step 8.4.2

Raise $3$ to the power of $2$ .

$x = \frac{\sqrt[3]{2} \sqrt[3]{9}}{3}$

Step 8.5

Simplify the numerator.

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Step 8.5.1

Combine using the product rule for radicals.

$x = \frac{\sqrt[3]{2 \cdot 9}}{3}$

Step 8.5.2

Multiply $2$ by $9$ .

$x = \frac{\sqrt[3]{18}}{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt[3]{18}}{3}$

Decimal Form:

$x = 0.87358046 \dots$