Pre-Algebra Examples

$\sqrt[12]{b} \sqrt[6]{b}$

Step 1

Multiply $\sqrt[12]{b} \sqrt[6]{b}$ .

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Step 1.1

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

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Step 1.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{b}$ as $b^{\frac{1}{6}}$ .

$\sqrt[12]{b} b^{\frac{1}{6}}$

Step 1.1.2

Rewrite $b^{\frac{1}{6}}$ as $b^{\frac{2}{12}}$ .

$\sqrt[12]{b} b^{\frac{2}{12}}$

Step 1.1.3

Rewrite $b^{\frac{2}{12}}$ as $\sqrt[12]{b^{2}}$ .

$\sqrt[12]{b} \sqrt[12]{b^{2}}$

Step 1.2

Combine using the product rule for radicals.

$\sqrt[12]{b \cdot b^{2}}$

Step 1.3

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

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Step 1.3.1

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

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Step 1.3.1.1

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

$\sqrt[12]{b^{1} b^{2}}$

Step 1.3.1.2

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

$\sqrt[12]{b^{1 + 2}}$

Step 1.3.2

Add $1$ and $2$ .

$\sqrt[12]{b^{3}}$

Step 2

Rewrite $\sqrt[12]{b^{3}}$ as $\sqrt[4]{\sqrt[3]{b^{3}}}$ .

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

Step 3

Pull terms out from under the radical, assuming real numbers.

$\sqrt[4]{b}$