Chapter 5 - Exponential Functions - 5.2 Solving Equations Using Exponent Rules - 5.2 Exercises - Page 437: 37

$x = -2$

$4^{x} = \frac{1}{16}$ $4^{x} = 16^{-1}$ $4^{x} = 4^{-2}$ $x = -2$ The student forgot that it is $4^{-2}$ and not $4^{2}$. This is where $4^{2} \ne \frac{1}{16}$ and that the student needs to remember that one over a number means that the number's power changes sign before proceeding to the next step. Check: $ = 4^{-2}$ $ = (\frac{1}{4})^{2}$ $ = \frac{1}{16}$