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}`