Simplify e^(- natural log of |x|)

$e^{- \ln (| x |)}$

Step 1

Simplify $- \ln (| x |)$ by moving $- 1$ inside the logarithm.

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

Step 2

Exponentiation and log are inverse functions.

${| x |}^{- 1}$

Step 3

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

$\frac{1}{| x |}$