Precalculus Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

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

Step 3

Exponentiation and log are inverse functions.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Move the negative in front of the fraction.

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

Step 5

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

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