Algebra Examples

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

Step 1

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

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Step 1.1

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

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Step 1.1.1

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

$\sqrt[4]{b^{3}} b^{\frac{1}{2}}$

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.2

Combine using the product rule for radicals.

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

Step 1.3

Multiply $b^{3}$ by $b^{2}$ by adding the exponents.

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Step 1.3.1

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

$\sqrt[4]{b^{3 + 2}}$

Step 1.3.2

Add $3$ and $2$ .

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

Step 2

Factor out $b^{4}$ .

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

Step 3

Pull terms out from under the radical.

$b \sqrt[4]{b}$