Algebra Examples

$\sqrt{\frac{p}{p^{- 3}}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Move $p^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt{p \cdot p^{3}}$

Step 1.2

Multiply $p$ by $p^{3}$ by adding the exponents.

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Step 1.2.1

Multiply $p$ by $p^{3}$ .

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Step 1.2.1.1

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

$\sqrt{p^{1} p^{3}}$

Step 1.2.1.2

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

$\sqrt{p^{1 + 3}}$

Step 1.2.2

Add $1$ and $3$ .

$\sqrt{p^{4}}$

Step 2

Rewrite $p^{4}$ as ${(p^{2})}^{2}$ .

$\sqrt{{(p^{2})}^{2}}$

Step 3

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

$p^{2}$