Precalculus Examples

$\sqrt[4]{b^{5}} \sqrt{b}$

Step 1

Factor out $b^{4}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $b \sqrt[4]{b} \sqrt{b}$ .

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Step 3.1

Rewrite the expression using the least common index of $4$ .

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Step 3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{b}$ as $b^{\frac{1}{2}}$ .

$b (b^{\frac{1}{2}} \sqrt[4]{b})$

Step 3.1.2

Rewrite $b^{\frac{1}{2}}$ as $b^{\frac{2}{4}}$ .

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

Step 3.1.3

Rewrite $b^{\frac{2}{4}}$ as $\sqrt[4]{b^{2}}$ .

$b (\sqrt[4]{b^{2}} \sqrt[4]{b})$

Step 3.2

Combine using the product rule for radicals.

$b \sqrt[4]{b^{2} b}$

Step 3.3

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

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Step 3.3.1

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

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Step 3.3.1.1

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

$b \sqrt[4]{b^{2} b^{1}}$

Step 3.3.1.2

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

$b \sqrt[4]{b^{2 + 1}}$

Step 3.3.2

Add $2$ and $1$ .

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