notice that, if you move a factor from the bottom to above, you'd change its sign, and if you move it from above to the bottom, you also have to change its sign, thus,
[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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[/tex]
[tex]\bf \cfrac{3(4x^4y^3)^2}{(5x^2y^6)^3}\impliedby \textit{first off, we distribute the exponent}
\\\\\\
\cfrac{3(4^2x^{4\cdot 2}y^{3\cdot 2})}{5^3x^{2\cdot 3}y^{6\cdot 3}}\implies \cfrac{3(16x^8y^6)}{125x^6y^{18}}\implies \cfrac{48x^8y^6}{125x^6y^{18}}\implies
\cfrac{48x^8x^{-6}}{125y^{18}y^{-6}}
\\\\\\
\cfrac{48x^{8-6}}{125y^{18-6}}\implies \cfrac{48x^2}{125y^{12}}[/tex]
