Question

How do I simplify 1/-5z^-5?

Answer 1

$\bf \cfrac{1}{-5z^{-5}}\\\\ -------------------------\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}}\qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \\ \quad \\ % negative exponential denominator a^{{ n}} \implies \cfrac{1}{a^{- n}} \qquad \qquad \cfrac{1}{a^{- n}}\implies \cfrac{1}{\frac{1}{a^{ n}}}\implies a^{{ n}} \\\\ -------------------------\\\\ thus$

$\bf -\cfrac{1}{5}\cdot \cfrac{1}{z^{-5}}\implies -\cfrac{1}{5}\cdot \cfrac{1}{\frac{1}{z^5}}\implies -\cfrac{1}{5}\cdot \cfrac{\frac{1}{1}}{\frac{1}{z^5}}\implies - \cfrac{1}{5}\cdot \cfrac{1}{1}\cdot \cfrac{z^5}{1} \\\\\\ -\cfrac{z^5}{5}$