Pre-Algebra Examples

$f (r^{4}) = \frac{13 x}{11 | x |}$

Step 1

Divide each term in $f r^{4} = \frac{13 x}{11 | x |}$ by $f$ and simplify.

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Step 1.1

Divide each term in $f r^{4} = \frac{13 x}{11 | x |}$ by $f$ .

$\frac{f r^{4}}{f} = \frac{\frac{13 x}{11 | x |}}{f}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $f$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{f r^{4}}{f} = \frac{\frac{13 x}{11 | x |}}{f}$

Step 1.2.1.2

Divide $r^{4}$ by $1$ .

$r^{4} = \frac{\frac{13 x}{11 | x |}}{f}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Multiply the numerator by the reciprocal of the denominator.

$r^{4} = \frac{13 x}{11 | x |} \cdot \frac{1}{f}$

Step 1.3.2

Multiply $\frac{13 x}{11 | x |}$ by $\frac{1}{f}$ .

$r^{4} = \frac{13 x}{11 | x | f}$

Step 1.3.3

Reorder factors in $\frac{13 x}{11 | x | f}$ .

$r^{4} = \frac{13 x}{11 f | x |}$

Step 2

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

$r = \pm \sqrt[4]{\frac{13 x}{11 f | x |}}$

Step 3

Simplify $\pm \sqrt[4]{\frac{13 x}{11 f | x |}}$ .

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Step 3.1

Rewrite $\sqrt[4]{\frac{13 x}{11 f | x |}}$ as $\frac{\sqrt[4]{13 x}}{\sqrt[4]{11 f | x |}}$ .

$r = \pm \frac{\sqrt[4]{13 x}}{\sqrt[4]{11 f | x |}}$

Step 3.2

Multiply $\frac{\sqrt[4]{13 x}}{\sqrt[4]{11 f | x |}}$ by $\frac{{\sqrt[4]{11 f | x |}}^{3}}{{\sqrt[4]{11 f | x |}}^{3}}$ .

$r = \pm \frac{\sqrt[4]{13 x}}{\sqrt[4]{11 f | x |}} \cdot \frac{{\sqrt[4]{11 f | x |}}^{3}}{{\sqrt[4]{11 f | x |}}^{3}}$

Step 3.3

Combine and simplify the denominator.

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Step 3.3.1

Multiply $\frac{\sqrt[4]{13 x}}{\sqrt[4]{11 f | x |}}$ by $\frac{{\sqrt[4]{11 f | x |}}^{3}}{{\sqrt[4]{11 f | x |}}^{3}}$ .

$r = \pm \frac{\sqrt[4]{13 x} {\sqrt[4]{11 f | x |}}^{3}}{\sqrt[4]{11 f | x |} {\sqrt[4]{11 f | x |}}^{3}}$

Step 3.3.2

Raise $\sqrt[4]{11 f | x |}$ to the power of $1$ .

$r = \pm \frac{\sqrt[4]{13 x} {\sqrt[4]{11 f | x |}}^{3}}{{\sqrt[4]{11 f | x |}}^{1} {\sqrt[4]{11 f | x |}}^{3}}$

Step 3.3.3

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

$r = \pm \frac{\sqrt[4]{13 x} {\sqrt[4]{11 f | x |}}^{3}}{{\sqrt[4]{11 f | x |}}^{1 + 3}}$

Step 3.3.4

Add $1$ and $3$ .

$r = \pm \frac{\sqrt[4]{13 x} {\sqrt[4]{11 f | x |}}^{3}}{{\sqrt[4]{11 f | x |}}^{4}}$

Step 3.3.5

Rewrite ${\sqrt[4]{11 f | x |}}^{4}$ as $11 f | x |$ .

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Step 3.3.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{11 f | x |}$ as ${(11 f | x |)}^{\frac{1}{4}}$ .

$r = \pm \frac{\sqrt[4]{13 x} {\sqrt[4]{11 f | x |}}^{3}}{{({(11 f | x |)}^{\frac{1}{4}})}^{4}}$

Step 3.3.5.2

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

$r = \pm \frac{\sqrt[4]{13 x} {\sqrt[4]{11 f | x |}}^{3}}{{(11 f | x |)}^{\frac{1}{4} \cdot 4}}$

Step 3.3.5.3

Combine $\frac{1}{4}$ and $4$ .

$r = \pm \frac{\sqrt[4]{13 x} {\sqrt[4]{11 f | x |}}^{3}}{{(11 f | x |)}^{\frac{4}{4}}}$

Step 3.3.5.4

Cancel the common factor of $4$ .

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Step 3.3.5.4.1

Cancel the common factor.

$r = \pm \frac{\sqrt[4]{13 x} {\sqrt[4]{11 f | x |}}^{3}}{{(11 f | x |)}^{\frac{4}{4}}}$

Step 3.3.5.4.2

Rewrite the expression.

$r = \pm \frac{\sqrt[4]{13 x} {\sqrt[4]{11 f | x |}}^{3}}{{(11 f | x |)}^{1}}$

Step 3.3.5.5

Simplify.

$r = \pm \frac{\sqrt[4]{13 x} {\sqrt[4]{11 f | x |}}^{3}}{11 f | x |}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Rewrite ${\sqrt[4]{11 f | x |}}^{3}$ as $\sqrt[4]{{(11 f | x |)}^{3}}$ .

$r = \pm \frac{\sqrt[4]{13 x} \sqrt[4]{{(11 f | x |)}^{3}}}{11 f | x |}$

Step 3.4.2

Apply the product rule to $11 f | x |$ .

$r = \pm \frac{\sqrt[4]{13 x} \sqrt[4]{{(11 f)}^{3} {| x |}^{3}}}{11 f | x |}$

Step 3.4.3

Apply the product rule to $11 f$ .

$r = \pm \frac{\sqrt[4]{13 x} \sqrt[4]{11^{3} f^{3} {| x |}^{3}}}{11 f | x |}$

Step 3.4.4

Raise $11$ to the power of $3$ .

$r = \pm \frac{\sqrt[4]{13 x} \sqrt[4]{1331 f^{3} {| x |}^{3}}}{11 f | x |}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Combine using the product rule for radicals.

$r = \pm \frac{\sqrt[4]{13 x (1331 f^{3} {| x |}^{3})}}{11 f | x |}$

Step 3.5.2

Multiply $1331$ by $13$ .

$r = \pm \frac{\sqrt[4]{17303 x (f^{3} {| x |}^{3})}}{11 f | x |}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Combine and simplify the denominator.

$r = \pm \frac{\sqrt[4]{13 x (1331 f^{3} {| x |}^{3})}}{11 f | x |}$

Step 3.6.2

Multiply $1331$ by $13$ .

$r = \pm \frac{\sqrt[4]{17303 x (f^{3} {| x |}^{3})}}{11 f | x |}$

Step 3.6.3

Remove unnecessary parentheses.

$r = \pm \frac{\sqrt[4]{17303 x f^{3} {| x |}^{3}}}{11 f | x |}$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$r = \frac{\sqrt[4]{17303 x f^{3} {| x |}^{3}}}{11 f | x |}$

Step 4.2

Next, use the negative value of the $\pm$ to find the second solution.

$r = - \frac{\sqrt[4]{17303 x f^{3} {| x |}^{3}}}{11 f | x |}$

Step 4.3

The complete solution is the result of both the positive and negative portions of the solution.

$r = \frac{\sqrt[4]{17303 x f^{3} {| x |}^{3}}}{11 f | x |}$

$r = - \frac{\sqrt[4]{17303 x f^{3} {| x |}^{3}}}{11 f | x |}$

$r = \frac{\sqrt[4]{17303 x f^{3} {| x |}^{3}}}{11 f | x |}$

$r = - \frac{\sqrt[4]{17303 x f^{3} {| x |}^{3}}}{11 f | x |}$