\( \displaystyle{4\,^4 \cdot 4\,^{-2} / 4 \; = \; {4\,^{4\,+\,(-2)} \over 4\,^1} \; = \; {4\,^{4\,-\,2} \over 4\,^1} \; = \; {4\,^2 \over 4\,^1} \, = \, 4\,^{2-1} \, = \, 4\,^1 \, = \, 4} \)