Precalculus Examples

$e^{- \frac{1}{2} \cdot \ln (16)}$

Step 1

Multiply $- \frac{1}{2} \ln (16)$ .

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Step 1.1

Reorder $\ln (16)$ and $\frac{1}{2}$ .

$e^{- (\frac{1}{2} \ln (16))}$

Step 1.2

Simplify $\frac{1}{2} \ln (16)$ by moving $\frac{1}{2}$ inside the logarithm.

$e^{- \ln (16^{\frac{1}{2}})}$

Step 2

Simplify $- \ln (16^{\frac{1}{2}})$ by moving $- 1$ inside the logarithm.

$e^{\ln ({(16^{\frac{1}{2}})}^{- 1})}$

Step 3

Exponentiation and log are inverse functions.

${(16^{\frac{1}{2}})}^{- 1}$

Step 4

Multiply the exponents in ${(16^{\frac{1}{2}})}^{- 1}$ .

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Step 4.1

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

$16^{\frac{1}{2} \cdot - 1}$

Step 4.2

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

$16^{\frac{- 1}{2}}$

Step 4.3

Move the negative in front of the fraction.

$16^{- \frac{1}{2}}$

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{16^{\frac{1}{2}}}$

Step 6

Simplify the denominator.

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Step 6.1

Rewrite $16$ as $4^{2}$ .

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

Step 6.2

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

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

Step 6.3

Cancel the common factor of $2$ .

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Step 6.3.1

Cancel the common factor.

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

Step 6.3.2

Rewrite the expression.

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

Step 6.4

Evaluate the exponent.

$\frac{1}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$