Pre-Algebra Examples

$3 x^{2} n x + 5 = 0$

Step 1

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

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Step 1.1

Move $x$ .

$3 (x \cdot x^{2}) n + 5 = 0$

Step 1.2

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

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Step 1.2.1

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

$3 (x^{1} x^{2}) n + 5 = 0$

Step 1.2.2

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

$3 x^{1 + 2} n + 5 = 0$

Step 1.3

Add $1$ and $2$ .

$3 x^{3} n + 5 = 0$

Step 2

Subtract $5$ from both sides of the equation.

$3 x^{3} n = - 5$

Step 3

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

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Step 3.1

Divide each term in $3 x^{3} n = - 5$ by $3 n$ .

$\frac{3 x^{3} n}{3 n} = \frac{- 5}{3 n}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 x^{3} n}{3 n} = \frac{- 5}{3 n}$

Step 3.2.1.2

Rewrite the expression.

$\frac{x^{3} n}{n} = \frac{- 5}{3 n}$

Step 3.2.2

Cancel the common factor of $n$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{x^{3} n}{n} = \frac{- 5}{3 n}$

Step 3.2.2.2

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

$x^{3} = \frac{- 5}{3 n}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$x^{3} = - \frac{5}{3 n}$

Step 4

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

$x = \sqrt[3]{- \frac{5}{3 n}}$

Step 5

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

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Step 5.1

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

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Step 5.1.1

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

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

Step 5.1.2

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

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

Step 5.2

Pull terms out from under the radical.

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

Step 5.3

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

$x = - \sqrt[3]{\frac{5}{3 n}}$

Step 5.4

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

$x = - \frac{\sqrt[3]{5}}{\sqrt[3]{3 n}}$

Step 5.5

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

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

Step 5.6

Combine and simplify the denominator.

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Step 5.6.1

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

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

Step 5.6.2

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

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

Step 5.6.3

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

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

Step 5.6.4

Add $1$ and $2$ .

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

Step 5.6.5

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

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Step 5.6.5.1

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

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

Step 5.6.5.2

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

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

Step 5.6.5.3

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

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

Step 5.6.5.4

Cancel the common factor of $3$ .

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Step 5.6.5.4.1

Cancel the common factor.

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

Step 5.6.5.4.2

Rewrite the expression.

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

Step 5.6.5.5

Simplify.

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

Step 5.7

Simplify the numerator.

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Step 5.7.1

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

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

Step 5.7.2

Apply the product rule to $3 n$ .

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

Step 5.7.3

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

$x = - \frac{\sqrt[3]{5} \sqrt[3]{9 n^{2}}}{3 n}$

Step 5.8

Simplify the numerator.

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Step 5.8.1

Combine using the product rule for radicals.

$x = - \frac{\sqrt[3]{5 (9 n^{2})}}{3 n}$

Step 5.8.2

Multiply $5$ by $9$ .

$x = - \frac{\sqrt[3]{45 n^{2}}}{3 n}$