Question

Utilize exponent rules to simplify the following 10x^3y^4 over 4xy^7

Answer 1

$\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}$

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.

$\bf \cfrac{10x^3y^4}{4xy^7}\implies \cfrac{10x^3y^4}{4x^1y^7}\implies \cfrac{10}{4}\cdot \cfrac{x^3y^4}{x^1y^7}\implies \cfrac{5}{2}\cdot \cfrac{x^3x^{-1}y^4y^{-7}}{1} \\\\\\ \cfrac{5}{2}\cdot x^{3-1}y^{4-7}\implies \cfrac{5}{2}x^2y^{-3}\implies \cfrac{5x^2y^{-3}}{2}\implies \cfrac{5x^2}{2y^3}$