Algebra Examples

$z = \frac{3 π y^{3}}{12}$

Step 1

Rewrite the equation as $\frac{3 π y^{3}}{12} = z$ .

$\frac{3 π y^{3}}{12} = z$

Step 2

Cancel the common factor of $3$ and $12$ .

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Step 2.1

Factor $3$ out of $3 π y^{3}$ .

$\frac{3 (π y^{3})}{12} = z$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $12$ .

$\frac{3 (π y^{3})}{3 \cdot 4} = z$

Step 2.2.2

Cancel the common factor.

$\frac{3 (π y^{3})}{3 \cdot 4} = z$

Step 2.2.3

Rewrite the expression.

$\frac{π y^{3}}{4} = z$

Step 3

Multiply both sides by $4$ .

$\frac{π y^{3}}{4} \cdot 4 = z \cdot 4$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{π y^{3}}{4} \cdot 4 = z \cdot 4$

Step 4.1.1.2

Rewrite the expression.

$π y^{3} = z \cdot 4$

Step 4.2

Simplify the right side.

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Step 4.2.1

Move $4$ to the left of $z$ .

$π y^{3} = 4 z$

Step 5

Solve for $y$ .

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Step 5.1

Divide each term in $π y^{3} = 4 z$ by $π$ and simplify.

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Step 5.1.1

Divide each term in $π y^{3} = 4 z$ by $π$ .

$\frac{π y^{3}}{π} = \frac{4 z}{π}$

Step 5.1.2

Simplify the left side.

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Step 5.1.2.1

Cancel the common factor of $π$ .

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Step 5.1.2.1.1

Cancel the common factor.

$\frac{π y^{3}}{π} = \frac{4 z}{π}$

Step 5.1.2.1.2

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

$y^{3} = \frac{4 z}{π}$

Step 5.2

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

$y = \sqrt[3]{\frac{4 z}{π}}$

Step 5.3

Simplify $\sqrt[3]{\frac{4 z}{π}}$ .

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Step 5.3.1

Rewrite $\sqrt[3]{\frac{4 z}{π}}$ as $\frac{\sqrt[3]{4 z}}{\sqrt[3]{π}}$ .

$y = \frac{\sqrt[3]{4 z}}{\sqrt[3]{π}}$

Step 5.3.2

Multiply $\frac{\sqrt[3]{4 z}}{\sqrt[3]{π}}$ by $\frac{{\sqrt[3]{π}}^{2}}{{\sqrt[3]{π}}^{2}}$ .

$y = \frac{\sqrt[3]{4 z}}{\sqrt[3]{π}} \cdot \frac{{\sqrt[3]{π}}^{2}}{{\sqrt[3]{π}}^{2}}$

Step 5.3.3

Combine and simplify the denominator.

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Step 5.3.3.1

Multiply $\frac{\sqrt[3]{4 z}}{\sqrt[3]{π}}$ by $\frac{{\sqrt[3]{π}}^{2}}{{\sqrt[3]{π}}^{2}}$ .

$y = \frac{\sqrt[3]{4 z} {\sqrt[3]{π}}^{2}}{\sqrt[3]{π} {\sqrt[3]{π}}^{2}}$

Step 5.3.3.2

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

$y = \frac{\sqrt[3]{4 z} {\sqrt[3]{π}}^{2}}{{\sqrt[3]{π}}^{1} {\sqrt[3]{π}}^{2}}$

Step 5.3.3.3

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

$y = \frac{\sqrt[3]{4 z} {\sqrt[3]{π}}^{2}}{{\sqrt[3]{π}}^{1 + 2}}$

Step 5.3.3.4

Add $1$ and $2$ .

$y = \frac{\sqrt[3]{4 z} {\sqrt[3]{π}}^{2}}{{\sqrt[3]{π}}^{3}}$

Step 5.3.3.5

Rewrite ${\sqrt[3]{π}}^{3}$ as $π$ .

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Step 5.3.3.5.1

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

$y = \frac{\sqrt[3]{4 z} {\sqrt[3]{π}}^{2}}{{(π^{\frac{1}{3}})}^{3}}$

Step 5.3.3.5.2

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

$y = \frac{\sqrt[3]{4 z} {\sqrt[3]{π}}^{2}}{π^{\frac{1}{3} \cdot 3}}$

Step 5.3.3.5.3

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

$y = \frac{\sqrt[3]{4 z} {\sqrt[3]{π}}^{2}}{π^{\frac{3}{3}}}$

Step 5.3.3.5.4

Cancel the common factor of $3$ .

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Step 5.3.3.5.4.1

Cancel the common factor.

$y = \frac{\sqrt[3]{4 z} {\sqrt[3]{π}}^{2}}{π^{\frac{3}{3}}}$

Step 5.3.3.5.4.2

Rewrite the expression.

$y = \frac{\sqrt[3]{4 z} {\sqrt[3]{π}}^{2}}{π^{1}}$

Step 5.3.3.5.5

Simplify.

$y = \frac{\sqrt[3]{4 z} {\sqrt[3]{π}}^{2}}{π}$

Step 5.3.4

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

$y = \frac{\sqrt[3]{4 z} \sqrt[3]{π^{2}}}{π}$

Step 5.3.5

Combine using the product rule for radicals.

$y = \frac{\sqrt[3]{4 z π^{2}}}{π}$