[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\qquad \qquad
a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}
\\\\
-------------------------------\\\\[/tex]
[tex]\bf \cfrac{x^ay^{-b}z^c}{x^{-d}y^ez^f}\implies \cfrac{x^ax^dz^cz^{-f}}{y^ey^b}\implies \cfrac{x^{a+d}z^{c-f}}{y^{e+b}}\\\\
-------------------------------\\\\
\cfrac{q^{\frac{33}{4}}}{q^8}\implies q^{\frac{33}{4}}\cdot q^{-8}\implies q^{\frac{33}{4}-8}\implies q^{\frac{1}{4}}[/tex]
