Precalculus Examples

$e^{(\frac{1}{2}) \ln (4)}$

Step 1

Simplify $(\frac{1}{2}) \ln (4)$ by moving $\frac{1}{2}$ inside the logarithm.

$e^{\ln (4^{\frac{1}{2}})}$

Step 2

Exponentiation and log are inverse functions.

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

Step 3

Simplify the expression.

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Step 3.1

Rewrite $4$ as $2^{2}$ .

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

Step 3.2

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

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

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$2^{1}$

Step 5

Evaluate the exponent.

$2$