Basic Math Examples

$2 c^{2} \cdot (3 c) - 5 = 0$

Step 1

Simplify each term.

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Step 1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 3 c^{2} c - 5 = 0$

Step 1.2

Multiply $c^{2}$ by $c$ by adding the exponents.

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Step 1.2.1

Move $c$ .

$2 \cdot 3 (c \cdot c^{2}) - 5 = 0$

Step 1.2.2

Multiply $c$ by $c^{2}$ .

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Step 1.2.2.1

Raise $c$ to the power of $1$ .

$2 \cdot 3 (c^{1} c^{2}) - 5 = 0$

Step 1.2.2.2

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

$2 \cdot 3 c^{1 + 2} - 5 = 0$

Step 1.2.3

Add $1$ and $2$ .

$2 \cdot 3 c^{3} - 5 = 0$

Step 1.3

Multiply $2$ by $3$ .

$6 c^{3} - 5 = 0$

Step 2

Add $5$ to both sides of the equation.

$6 c^{3} = 5$

Step 3

Divide each term in $6 c^{3} = 5$ by $6$ and simplify.

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Step 3.1

Divide each term in $6 c^{3} = 5$ by $6$ .

$\frac{6 c^{3}}{6} = \frac{5}{6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6 c^{3}}{6} = \frac{5}{6}$

Step 3.2.1.2

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

$c^{3} = \frac{5}{6}$

Step 4

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

$c = \sqrt[3]{\frac{5}{6}}$

Step 5

Simplify $\sqrt[3]{\frac{5}{6}}$ .

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Step 5.1

Rewrite $\sqrt[3]{\frac{5}{6}}$ as $\frac{\sqrt[3]{5}}{\sqrt[3]{6}}$ .

$c = \frac{\sqrt[3]{5}}{\sqrt[3]{6}}$

Step 5.2

Multiply $\frac{\sqrt[3]{5}}{\sqrt[3]{6}}$ by $\frac{{\sqrt[3]{6}}^{2}}{{\sqrt[3]{6}}^{2}}$ .

$c = \frac{\sqrt[3]{5}}{\sqrt[3]{6}} \cdot \frac{{\sqrt[3]{6}}^{2}}{{\sqrt[3]{6}}^{2}}$

Step 5.3

Combine and simplify the denominator.

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Step 5.3.1

Multiply $\frac{\sqrt[3]{5}}{\sqrt[3]{6}}$ by $\frac{{\sqrt[3]{6}}^{2}}{{\sqrt[3]{6}}^{2}}$ .

$c = \frac{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}{\sqrt[3]{6} {\sqrt[3]{6}}^{2}}$

Step 5.3.2

Raise $\sqrt[3]{6}$ to the power of $1$ .

$c = \frac{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}{{\sqrt[3]{6}}^{1} {\sqrt[3]{6}}^{2}}$

Step 5.3.3

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

$c = \frac{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}{{\sqrt[3]{6}}^{1 + 2}}$

Step 5.3.4

Add $1$ and $2$ .

$c = \frac{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}{{\sqrt[3]{6}}^{3}}$

Step 5.3.5

Rewrite ${\sqrt[3]{6}}^{3}$ as $6$ .

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Step 5.3.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{6}$ as $6^{\frac{1}{3}}$ .

$c = \frac{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}{{(6^{\frac{1}{3}})}^{3}}$

Step 5.3.5.2

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

$c = \frac{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}{6^{\frac{1}{3} \cdot 3}}$

Step 5.3.5.3

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

$c = \frac{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}{6^{\frac{3}{3}}}$

Step 5.3.5.4

Cancel the common factor of $3$ .

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Step 5.3.5.4.1

Cancel the common factor.

$c = \frac{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}{6^{\frac{3}{3}}}$

Step 5.3.5.4.2

Rewrite the expression.

$c = \frac{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}{6^{1}}$

Step 5.3.5.5

Evaluate the exponent.

$c = \frac{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}{6}$

Step 5.4

Simplify the numerator.

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Step 5.4.1

Rewrite ${\sqrt[3]{6}}^{2}$ as $\sqrt[3]{6^{2}}$ .

$c = \frac{\sqrt[3]{5} \sqrt[3]{6^{2}}}{6}$

Step 5.4.2

Raise $6$ to the power of $2$ .

$c = \frac{\sqrt[3]{5} \sqrt[3]{36}}{6}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Combine using the product rule for radicals.

$c = \frac{\sqrt[3]{5 \cdot 36}}{6}$

Step 5.5.2

Multiply $5$ by $36$ .

$c = \frac{\sqrt[3]{180}}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$c = \frac{\sqrt[3]{180}}{6}$

Decimal Form:

$c = 0.94103602 \dots$