[tex]\bf \cfrac{12x^{-3}y^5z^{-7}}{4x^{-2}y^4z^6}\\\\
-----------------------------\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}\\ \quad \\a^{{ n}} \implies \cfrac{1}{a^{- n}}
\qquad \qquad
\cfrac{1}{a^{- n}}\implies \cfrac{1}{\frac{1}{a^{ n}}}\implies a^{{ n}}\\\\
-----------------------------\\\\[/tex]
[tex]\bf thus
\\\\\\
\cfrac{12\frac{1}{x^3}y^5\frac{1}{z^7}}{4\frac{1}{x^2}y^4z^6}\implies
\cfrac{\frac{12y^5}{x^3z^7}}{\frac{4y^4z^6}{x^2}}\implies \cfrac{12y^5}{x^3z^7}\times \cfrac{x^2}{4y^4z^6}\implies \cfrac{12y^5x^2}{4x^3y^4z^7z^6}
\\\\\\
\cfrac{12}{4}\cdot \cfrac{x^2}{x^3}\cdot \cfrac{y^5}{y^4}\cdot \cfrac{1}{z^7z^6}\implies 3\cdot \cfrac{1}{x}\cdot \cfrac{y}{1}\cdot \cfrac{1}{z^{7+6}}\implies \cfrac{3y}{xz^{13}}[/tex]
