Finite Math Examples

$\frac{4 b}{\sqrt[4]{7 a^{3}}}$

Step 1

Multiply $\frac{4 b}{\sqrt[4]{7 a^{3}}}$ by $\frac{{\sqrt[4]{7 a^{3}}}^{3}}{{\sqrt[4]{7 a^{3}}}^{3}}$ .

$\frac{4 b}{\sqrt[4]{7 a^{3}}} \cdot \frac{{\sqrt[4]{7 a^{3}}}^{3}}{{\sqrt[4]{7 a^{3}}}^{3}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{4 b}{\sqrt[4]{7 a^{3}}}$ by $\frac{{\sqrt[4]{7 a^{3}}}^{3}}{{\sqrt[4]{7 a^{3}}}^{3}}$ .

$\frac{4 b {\sqrt[4]{7 a^{3}}}^{3}}{\sqrt[4]{7 a^{3}} {\sqrt[4]{7 a^{3}}}^{3}}$

Step 2.2

Raise $\sqrt[4]{7 a^{3}}$ to the power of $1$ .

$\frac{4 b {\sqrt[4]{7 a^{3}}}^{3}}{{\sqrt[4]{7 a^{3}}}^{1} {\sqrt[4]{7 a^{3}}}^{3}}$

Step 2.3

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

$\frac{4 b {\sqrt[4]{7 a^{3}}}^{3}}{{\sqrt[4]{7 a^{3}}}^{1 + 3}}$

Step 2.4

Add $1$ and $3$ .

$\frac{4 b {\sqrt[4]{7 a^{3}}}^{3}}{{\sqrt[4]{7 a^{3}}}^{4}}$

Step 2.5

Rewrite ${\sqrt[4]{7 a^{3}}}^{4}$ as $7 a^{3}$ .

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Step 2.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{7 a^{3}}$ as ${(7 a^{3})}^{\frac{1}{4}}$ .

$\frac{4 b {\sqrt[4]{7 a^{3}}}^{3}}{{({(7 a^{3})}^{\frac{1}{4}})}^{4}}$

Step 2.5.2

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

$\frac{4 b {\sqrt[4]{7 a^{3}}}^{3}}{{(7 a^{3})}^{\frac{1}{4} \cdot 4}}$

Step 2.5.3

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

$\frac{4 b {\sqrt[4]{7 a^{3}}}^{3}}{{(7 a^{3})}^{\frac{4}{4}}}$

Step 2.5.4

Cancel the common factor of $4$ .

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Step 2.5.4.1

Cancel the common factor.

$\frac{4 b {\sqrt[4]{7 a^{3}}}^{3}}{{(7 a^{3})}^{\frac{4}{4}}}$

Step 2.5.4.2

Rewrite the expression.

$\frac{4 b {\sqrt[4]{7 a^{3}}}^{3}}{{(7 a^{3})}^{1}}$

Step 2.5.5

Simplify.

$\frac{4 b {\sqrt[4]{7 a^{3}}}^{3}}{7 a^{3}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite ${\sqrt[4]{7 a^{3}}}^{3}$ as $\sqrt[4]{{(7 a^{3})}^{3}}$ .

$\frac{4 b \sqrt[4]{{(7 a^{3})}^{3}}}{7 a^{3}}$

Step 3.2

Apply the product rule to $7 a^{3}$ .

$\frac{4 b \sqrt[4]{7^{3} {(a^{3})}^{3}}}{7 a^{3}}$

Step 3.3

Raise $7$ to the power of $3$ .

$\frac{4 b \sqrt[4]{343 {(a^{3})}^{3}}}{7 a^{3}}$

Step 3.4

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

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Step 3.4.1

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

$\frac{4 b \sqrt[4]{343 a^{3 \cdot 3}}}{7 a^{3}}$

Step 3.4.2

Multiply $3$ by $3$ .

$\frac{4 b \sqrt[4]{343 a^{9}}}{7 a^{3}}$

Step 3.5

Rewrite $343 a^{9}$ as ${(a^{2})}^{4} \cdot (343 a)$ .

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Step 3.5.1

Factor out $a^{8}$ .

$\frac{4 b \sqrt[4]{343 (a^{8} a)}}{7 a^{3}}$

Step 3.5.2

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

$\frac{4 b \sqrt[4]{343 ({(a^{2})}^{4} a)}}{7 a^{3}}$

Step 3.5.3

Reorder $343$ and ${(a^{2})}^{4}$ .

$\frac{4 b \sqrt[4]{{(a^{2})}^{4} \cdot 343 a}}{7 a^{3}}$

Step 3.5.4

Add parentheses.

$\frac{4 b \sqrt[4]{{(a^{2})}^{4} \cdot (343 a)}}{7 a^{3}}$

Step 3.6

Pull terms out from under the radical.

$\frac{4 b a^{2} \sqrt[4]{343 a}}{7 a^{3}}$

Step 4

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

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Step 4.1

Factor $a^{2}$ out of $4 b a^{2} \sqrt[4]{343 a}$ .

$\frac{a^{2} (4 b \sqrt[4]{343 a})}{7 a^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a^{2}$ out of $7 a^{3}$ .

$\frac{a^{2} (4 b \sqrt[4]{343 a})}{a^{2} (7 a)}$

Step 4.2.2

Cancel the common factor.

$\frac{a^{2} (4 b \sqrt[4]{343 a})}{a^{2} (7 a)}$

Step 4.2.3

Rewrite the expression.

$\frac{4 b \sqrt[4]{343 a}}{7 a}$