Basic Math Examples

$w^{3} \cdot \frac{5}{6} = 2 \frac{1}{3}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $w^{3} \cdot \frac{5}{6}$ .

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Step 1.1.1

Combine $w^{3}$ and $\frac{5}{6}$ .

$\frac{w^{3} \cdot 5}{6} = 2 \frac{1}{3}$

Step 1.1.2

Move $5$ to the left of $w^{3}$ .

$\frac{5 w^{3}}{6} = 2 \frac{1}{3}$

Step 2

Simplify the right side.

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Step 2.1

Convert $2 \frac{1}{3}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{5 w^{3}}{6} = 2 + \frac{1}{3}$

Step 2.1.2

Add $2$ and $\frac{1}{3}$ .

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Step 2.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 w^{3}}{6} = 2 \cdot \frac{3}{3} + \frac{1}{3}$

Step 2.1.2.2

Combine $2$ and $\frac{3}{3}$ .

$\frac{5 w^{3}}{6} = \frac{2 \cdot 3}{3} + \frac{1}{3}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{5 w^{3}}{6} = \frac{2 \cdot 3 + 1}{3}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $2$ by $3$ .

$\frac{5 w^{3}}{6} = \frac{6 + 1}{3}$

Step 2.1.2.4.2

Add $6$ and $1$ .

$\frac{5 w^{3}}{6} = \frac{7}{3}$

Step 3

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} \cdot \frac{5 w^{3}}{6} = \frac{6}{5} \cdot \frac{7}{3}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{6}{5} \cdot \frac{5 w^{3}}{6}$ .

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Step 4.1.1.1

Combine.

$\frac{6 (5 w^{3})}{5 \cdot 6} = \frac{6}{5} \cdot \frac{7}{3}$

Step 4.1.1.2

Cancel the common factor of $6$ .

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Step 4.1.1.2.1

Cancel the common factor.

$\frac{6 (5 w^{3})}{5 \cdot 6} = \frac{6}{5} \cdot \frac{7}{3}$

Step 4.1.1.2.2

Rewrite the expression.

$\frac{5 w^{3}}{5} = \frac{6}{5} \cdot \frac{7}{3}$

Step 4.1.1.3

Cancel the common factor of $5$ .

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Step 4.1.1.3.1

Cancel the common factor.

$\frac{5 w^{3}}{5} = \frac{6}{5} \cdot \frac{7}{3}$

Step 4.1.1.3.2

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

$w^{3} = \frac{6}{5} \cdot \frac{7}{3}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{6}{5} \cdot \frac{7}{3}$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

Factor $3$ out of $6$ .

$w^{3} = \frac{3 (2)}{5} \cdot \frac{7}{3}$

Step 4.2.1.1.2

Cancel the common factor.

$w^{3} = \frac{3 \cdot 2}{5} \cdot \frac{7}{3}$

Step 4.2.1.1.3

Rewrite the expression.

$w^{3} = \frac{2}{5} \cdot 7$

Step 4.2.1.2

Combine $\frac{2}{5}$ and $7$ .

$w^{3} = \frac{2 \cdot 7}{5}$

Step 4.2.1.3

Multiply $2$ by $7$ .

$w^{3} = \frac{14}{5}$

Step 5

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

$w = \sqrt[3]{\frac{14}{5}}$

Step 6

Simplify $\sqrt[3]{\frac{14}{5}}$ .

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Step 6.1

Rewrite $\sqrt[3]{\frac{14}{5}}$ as $\frac{\sqrt[3]{14}}{\sqrt[3]{5}}$ .

$w = \frac{\sqrt[3]{14}}{\sqrt[3]{5}}$

Step 6.2

Multiply $\frac{\sqrt[3]{14}}{\sqrt[3]{5}}$ by $\frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$ .

$w = \frac{\sqrt[3]{14}}{\sqrt[3]{5}} \cdot \frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$

Step 6.3

Combine and simplify the denominator.

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Step 6.3.1

Multiply $\frac{\sqrt[3]{14}}{\sqrt[3]{5}}$ by $\frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$ .

$w = \frac{\sqrt[3]{14} {\sqrt[3]{5}}^{2}}{\sqrt[3]{5} {\sqrt[3]{5}}^{2}}$

Step 6.3.2

Raise $\sqrt[3]{5}$ to the power of $1$ .

$w = \frac{\sqrt[3]{14} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{1} {\sqrt[3]{5}}^{2}}$

Step 6.3.3

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

$w = \frac{\sqrt[3]{14} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{1 + 2}}$

Step 6.3.4

Add $1$ and $2$ .

$w = \frac{\sqrt[3]{14} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{3}}$

Step 6.3.5

Rewrite ${\sqrt[3]{5}}^{3}$ as $5$ .

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Step 6.3.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5}$ as $5^{\frac{1}{3}}$ .

$w = \frac{\sqrt[3]{14} {\sqrt[3]{5}}^{2}}{{(5^{\frac{1}{3}})}^{3}}$

Step 6.3.5.2

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

$w = \frac{\sqrt[3]{14} {\sqrt[3]{5}}^{2}}{5^{\frac{1}{3} \cdot 3}}$

Step 6.3.5.3

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

$w = \frac{\sqrt[3]{14} {\sqrt[3]{5}}^{2}}{5^{\frac{3}{3}}}$

Step 6.3.5.4

Cancel the common factor of $3$ .

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Step 6.3.5.4.1

Cancel the common factor.

$w = \frac{\sqrt[3]{14} {\sqrt[3]{5}}^{2}}{5^{\frac{3}{3}}}$

Step 6.3.5.4.2

Rewrite the expression.

$w = \frac{\sqrt[3]{14} {\sqrt[3]{5}}^{2}}{5^{1}}$

Step 6.3.5.5

Evaluate the exponent.

$w = \frac{\sqrt[3]{14} {\sqrt[3]{5}}^{2}}{5}$

Step 6.4

Simplify the numerator.

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Step 6.4.1

Rewrite ${\sqrt[3]{5}}^{2}$ as $\sqrt[3]{5^{2}}$ .

$w = \frac{\sqrt[3]{14} \sqrt[3]{5^{2}}}{5}$

Step 6.4.2

Raise $5$ to the power of $2$ .

$w = \frac{\sqrt[3]{14} \sqrt[3]{25}}{5}$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Combine using the product rule for radicals.

$w = \frac{\sqrt[3]{14 \cdot 25}}{5}$

Step 6.5.2

Multiply $14$ by $25$ .

$w = \frac{\sqrt[3]{350}}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$w = \frac{\sqrt[3]{350}}{5}$

Decimal Form:

$w = 1.40945974 \dots$