[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}}}}
\\\\
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\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}}
\\\\\\
and\qquad \qquad \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\\\\
-------------------------------\\\\[/tex]
[tex]\bf \cfrac{\frac{m^2n^3}{p^3}}{\frac{mp}{n^2}}\implies \cfrac{m^2n^3}{p^3}\cdot \cfrac{n^2}{mp}\implies \cfrac{m^2n^3n^2}{p^3m^1p^1}\implies \cfrac{m^2m^{-1} n^3n^2}{p^3p^1}
\\\\\\
\cfrac{m^{2-1}n^{3+2}}{p^{3+1}}\implies \cfrac{m^1n^5}{p^4}\implies \boxed{\cfrac{mn^5}{p^4}}[/tex]
