Pre-Algebra Examples

$\frac{- 4}{\sqrt[4]{3 b^{3}}}$

Step 1

Move the negative in front of the fraction.

$- \frac{4}{\sqrt[4]{3 b^{3}}}$

Step 2

Multiply $\frac{4}{\sqrt[4]{3 b^{3}}}$ by $\frac{{\sqrt[4]{3 b^{3}}}^{3}}{{\sqrt[4]{3 b^{3}}}^{3}}$ .

$- (\frac{4}{\sqrt[4]{3 b^{3}}} \cdot \frac{{\sqrt[4]{3 b^{3}}}^{3}}{{\sqrt[4]{3 b^{3}}}^{3}})$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{4}{\sqrt[4]{3 b^{3}}}$ by $\frac{{\sqrt[4]{3 b^{3}}}^{3}}{{\sqrt[4]{3 b^{3}}}^{3}}$ .

$- \frac{4 {\sqrt[4]{3 b^{3}}}^{3}}{\sqrt[4]{3 b^{3}} {\sqrt[4]{3 b^{3}}}^{3}}$

Step 3.2

Raise $\sqrt[4]{3 b^{3}}$ to the power of $1$ .

$- \frac{4 {\sqrt[4]{3 b^{3}}}^{3}}{{\sqrt[4]{3 b^{3}}}^{1} {\sqrt[4]{3 b^{3}}}^{3}}$

Step 3.3

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

$- \frac{4 {\sqrt[4]{3 b^{3}}}^{3}}{{\sqrt[4]{3 b^{3}}}^{1 + 3}}$

Step 3.4

Add $1$ and $3$ .

$- \frac{4 {\sqrt[4]{3 b^{3}}}^{3}}{{\sqrt[4]{3 b^{3}}}^{4}}$

Step 3.5

Rewrite ${\sqrt[4]{3 b^{3}}}^{4}$ as $3 b^{3}$ .

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Step 3.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{3 b^{3}}$ as ${(3 b^{3})}^{\frac{1}{4}}$ .

$- \frac{4 {\sqrt[4]{3 b^{3}}}^{3}}{{({(3 b^{3})}^{\frac{1}{4}})}^{4}}$

Step 3.5.2

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

$- \frac{4 {\sqrt[4]{3 b^{3}}}^{3}}{{(3 b^{3})}^{\frac{1}{4} \cdot 4}}$

Step 3.5.3

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

$- \frac{4 {\sqrt[4]{3 b^{3}}}^{3}}{{(3 b^{3})}^{\frac{4}{4}}}$

Step 3.5.4

Cancel the common factor of $4$ .

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Step 3.5.4.1

Cancel the common factor.

$- \frac{4 {\sqrt[4]{3 b^{3}}}^{3}}{{(3 b^{3})}^{\frac{4}{4}}}$

Step 3.5.4.2

Rewrite the expression.

$- \frac{4 {\sqrt[4]{3 b^{3}}}^{3}}{{(3 b^{3})}^{1}}$

Step 3.5.5

Simplify.

$- \frac{4 {\sqrt[4]{3 b^{3}}}^{3}}{3 b^{3}}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite ${\sqrt[4]{3 b^{3}}}^{3}$ as $\sqrt[4]{{(3 b^{3})}^{3}}$ .

$- \frac{4 \sqrt[4]{{(3 b^{3})}^{3}}}{3 b^{3}}$

Step 4.2

Apply the product rule to $3 b^{3}$ .

$- \frac{4 \sqrt[4]{3^{3} {(b^{3})}^{3}}}{3 b^{3}}$

Step 4.3

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

$- \frac{4 \sqrt[4]{27 {(b^{3})}^{3}}}{3 b^{3}}$

Step 4.4

Multiply the exponents in ${(b^{3})}^{3}$ .

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Step 4.4.1

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

$- \frac{4 \sqrt[4]{27 b^{3 \cdot 3}}}{3 b^{3}}$

Step 4.4.2

Multiply $3$ by $3$ .

$- \frac{4 \sqrt[4]{27 b^{9}}}{3 b^{3}}$

Step 4.5

Rewrite $27 b^{9}$ as ${(b^{2})}^{4} \cdot (27 b)$ .

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Step 4.5.1

Factor out $b^{8}$ .

$- \frac{4 \sqrt[4]{27 (b^{8} b)}}{3 b^{3}}$

Step 4.5.2

Rewrite $b^{8}$ as ${(b^{2})}^{4}$ .

$- \frac{4 \sqrt[4]{27 ({(b^{2})}^{4} b)}}{3 b^{3}}$

Step 4.5.3

Reorder $27$ and ${(b^{2})}^{4}$ .

$- \frac{4 \sqrt[4]{{(b^{2})}^{4} \cdot 27 b}}{3 b^{3}}$

Step 4.5.4

Add parentheses.

$- \frac{4 \sqrt[4]{{(b^{2})}^{4} \cdot (27 b)}}{3 b^{3}}$

Step 4.6

Pull terms out from under the radical.

$- \frac{4 b^{2} \sqrt[4]{27 b}}{3 b^{3}}$

Step 5

Cancel the common factor of $b^{2}$ and $b^{3}$ .

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Step 5.1

Factor $b^{2}$ out of $4 b^{2} \sqrt[4]{27 b}$ .

$- \frac{b^{2} (4 \sqrt[4]{27 b})}{3 b^{3}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $b^{2}$ out of $3 b^{3}$ .

$- \frac{b^{2} (4 \sqrt[4]{27 b})}{b^{2} (3 b)}$

Step 5.2.2

Cancel the common factor.

$- \frac{b^{2} (4 \sqrt[4]{27 b})}{b^{2} (3 b)}$

Step 5.2.3

Rewrite the expression.

$- \frac{4 \sqrt[4]{27 b}}{3 b}$