Algebra Examples

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

Step 1

Factor out $m^{2}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

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

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

Step 3.1.2

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

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

Step 3.1.3

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

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

Step 3.2

Combine using the product rule for radicals.

$m \sqrt[4]{m \cdot m^{2}}$

Step 3.3

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

Tap for more steps...

Step 3.3.1

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

Tap for more steps...

Step 3.3.1.1

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

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

Step 3.3.1.2

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

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

Step 3.3.2

Add $1$ and $2$ .

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