## Intermediate Algebra: Connecting Concepts through Application

$x = -2$
$4^{x} = \frac{1}{16}$ $4^{x} = 16^{-1}$ $4^{x} = 4^{-2}$ $x = -2$ 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: $= 4^{-2}$ $= (\frac{1}{4})^{2}$ $= \frac{1}{16}$