Precalculus Examples

$e^{4 \ln (\sqrt{p})}$

Step 1

Simplify $4 \ln (\sqrt{p})$ by moving $4$ inside the logarithm.

$e^{\ln ({\sqrt{p}}^{4})}$

Step 2

Exponentiation and log are inverse functions.

${\sqrt{p}}^{4}$

Step 3

Rewrite ${\sqrt{p}}^{4}$ as $p^{2}$ .

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Step 3.1

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

${(p^{\frac{1}{2}})}^{4}$

Step 3.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$p^{\frac{1}{2} \cdot 4}$

Step 3.3

Combine $\frac{1}{2}$ and $4$ .

$p^{\frac{4}{2}}$

Step 3.4

Cancel the common factor of $4$ and $2$ .

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Step 3.4.1

Factor $2$ out of $4$ .

$p^{\frac{2 \cdot 2}{2}}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $2$ out of $2$ .

$p^{\frac{2 \cdot 2}{2 (1)}}$

Step 3.4.2.2

Cancel the common factor.

$p^{\frac{2 \cdot 2}{2 \cdot 1}}$

Step 3.4.2.3

Rewrite the expression.

$p^{\frac{2}{1}}$

Step 3.4.2.4

Divide $2$ by $1$ .

$p^{2}$