Finite Math Examples

$\sqrt[3]{w} \cdot \sqrt[4]{w}$

Step 1

Rewrite the expression using the least common index of $12$ .

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Step 1.1

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

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

Step 1.2

Rewrite $w^{\frac{1}{3}}$ as $w^{\frac{4}{12}}$ .

$w^{\frac{4}{12}} \sqrt[4]{w}$

Step 1.3

Rewrite $w^{\frac{4}{12}}$ as $\sqrt[12]{w^{4}}$ .

$\sqrt[12]{w^{4}} \sqrt[4]{w}$

Step 1.4

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

$\sqrt[12]{w^{4}} w^{\frac{1}{4}}$

Step 1.5

Rewrite $w^{\frac{1}{4}}$ as $w^{\frac{3}{12}}$ .

$\sqrt[12]{w^{4}} w^{\frac{3}{12}}$

Step 1.6

Rewrite $w^{\frac{3}{12}}$ as $\sqrt[12]{w^{3}}$ .

$\sqrt[12]{w^{4}} \sqrt[12]{w^{3}}$

Step 2

Combine using the product rule for radicals.

$\sqrt[12]{w^{4} w^{3}}$

Step 3

Multiply $w^{4}$ by $w^{3}$ by adding the exponents.

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Step 3.1

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

$\sqrt[12]{w^{4 + 3}}$

Step 3.2

Add $4$ and $3$ .

$\sqrt[12]{w^{7}}$