Algebra Examples

$\sqrt[4]{p} \cdot \sqrt{p^{3}}$

Step 1

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

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{p^{3}}$ as $p^{\frac{3}{2}}$ .

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

Step 1.2

Rewrite $p^{\frac{3}{2}}$ as $p^{\frac{6}{4}}$ .

$\sqrt[4]{p} \cdot p^{\frac{6}{4}}$

Step 1.3

Rewrite $p^{\frac{6}{4}}$ as $\sqrt[4]{p^{6}}$ .

$\sqrt[4]{p} \cdot \sqrt[4]{p^{6}}$

Step 2

Combine using the product rule for radicals.

$\sqrt[4]{p \cdot p^{6}}$

Step 3

Multiply $p$ by $p^{6}$ by adding the exponents.

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Step 3.1

Multiply $p$ by $p^{6}$ .

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Step 3.1.1

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

$\sqrt[4]{p^{1} p^{6}}$

Step 3.1.2

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

$\sqrt[4]{p^{1 + 6}}$

Step 3.2

Add $1$ and $6$ .

$\sqrt[4]{p^{7}}$