Respuesta :
[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]
so, in short, if you move a factor from the bottom to the top, or the other way around, from the top to the bottom, then you change the sign of the exponent.
[tex]\bf \cfrac{10x^3y^4}{4xy^7}\implies \cfrac{10x^3y^4}{4x^1y^7}\implies \cfrac{10}{4}\cdot \cfrac{x^3y^4}{x^1y^7}\implies \cfrac{5}{2}\cdot \cfrac{x^3x^{-1}y^4y^{-7}}{1} \\\\\\ \cfrac{5}{2}\cdot x^{3-1}y^{4-7}\implies \cfrac{5}{2}x^2y^{-3}\implies \cfrac{5x^2y^{-3}}{2}\implies \cfrac{5x^2}{2y^3}[/tex]
so, in short, if you move a factor from the bottom to the top, or the other way around, from the top to the bottom, then you change the sign of the exponent.
[tex]\bf \cfrac{10x^3y^4}{4xy^7}\implies \cfrac{10x^3y^4}{4x^1y^7}\implies \cfrac{10}{4}\cdot \cfrac{x^3y^4}{x^1y^7}\implies \cfrac{5}{2}\cdot \cfrac{x^3x^{-1}y^4y^{-7}}{1} \\\\\\ \cfrac{5}{2}\cdot x^{3-1}y^{4-7}\implies \cfrac{5}{2}x^2y^{-3}\implies \cfrac{5x^2y^{-3}}{2}\implies \cfrac{5x^2}{2y^3}[/tex]
