Basic Math Examples

$5 c^{3} = - 2$

Step 1

Divide each term in $5 c^{3} = - 2$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 c^{3} = - 2$ by $5$ .

$\frac{5 c^{3}}{5} = \frac{- 2}{5}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 c^{3}}{5} = \frac{- 2}{5}$

Step 1.2.1.2

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

$c^{3} = \frac{- 2}{5}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Move the negative in front of the fraction.

$c^{3} = - \frac{2}{5}$

Step 2

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

$c = \sqrt[3]{- \frac{2}{5}}$

Step 3

Simplify $\sqrt[3]{- \frac{2}{5}}$ .

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Step 3.1

Rewrite $- \frac{2}{5}$ as ${({(- 1)}^{3})}^{3} \frac{2}{5}$ .

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Step 3.1.1

Rewrite $- 1$ as ${(- 1)}^{3}$ .

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

Step 3.1.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

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

Step 3.2

Pull terms out from under the radical.

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

Step 3.3

Raise $- 1$ to the power of $3$ .

$c = - \sqrt[3]{\frac{2}{5}}$

Step 3.4

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

$c = - \frac{\sqrt[3]{2}}{\sqrt[3]{5}}$

Step 3.5

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

$c = - (\frac{\sqrt[3]{2}}{\sqrt[3]{5}} \cdot \frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}})$

Step 3.6

Combine and simplify the denominator.

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Step 3.6.1

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

$c = - \frac{\sqrt[3]{2} {\sqrt[3]{5}}^{2}}{\sqrt[3]{5} {\sqrt[3]{5}}^{2}}$

Step 3.6.2

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

$c = - \frac{\sqrt[3]{2} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{1} {\sqrt[3]{5}}^{2}}$

Step 3.6.3

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

$c = - \frac{\sqrt[3]{2} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{1 + 2}}$

Step 3.6.4

Add $1$ and $2$ .

$c = - \frac{\sqrt[3]{2} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{3}}$

Step 3.6.5

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

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Step 3.6.5.1

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

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

Step 3.6.5.2

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

$c = - \frac{\sqrt[3]{2} {\sqrt[3]{5}}^{2}}{5^{\frac{1}{3} \cdot 3}}$

Step 3.6.5.3

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

$c = - \frac{\sqrt[3]{2} {\sqrt[3]{5}}^{2}}{5^{\frac{3}{3}}}$

Step 3.6.5.4

Cancel the common factor of $3$ .

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Step 3.6.5.4.1

Cancel the common factor.

$c = - \frac{\sqrt[3]{2} {\sqrt[3]{5}}^{2}}{5^{\frac{3}{3}}}$

Step 3.6.5.4.2

Rewrite the expression.

$c = - \frac{\sqrt[3]{2} {\sqrt[3]{5}}^{2}}{5^{1}}$

Step 3.6.5.5

Evaluate the exponent.

$c = - \frac{\sqrt[3]{2} {\sqrt[3]{5}}^{2}}{5}$

Step 3.7

Simplify the numerator.

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Step 3.7.1

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

$c = - \frac{\sqrt[3]{2} \sqrt[3]{5^{2}}}{5}$

Step 3.7.2

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

$c = - \frac{\sqrt[3]{2} \sqrt[3]{25}}{5}$

Step 3.8

Simplify the numerator.

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Step 3.8.1

Combine using the product rule for radicals.

$c = - \frac{\sqrt[3]{2 \cdot 25}}{5}$

Step 3.8.2

Multiply $2$ by $25$ .

$c = - \frac{\sqrt[3]{50}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$c = - \frac{\sqrt[3]{50}}{5}$

Decimal Form:

$c = - 0.73680629 \dots$