Question

Find the quotient of 21x^2y^6+6xy^3-30xy/3xy.

a)21x^2y^6+6xy^3-10
b)7xy^5+2y^2+10
c)7xy^5+2y^2-10
d)7xy^5+2y-10

Answer 1

Explanation:

It’s c

Answer 2

`\bf ~~~~~~~~~~~~\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)} \\\\ -------------------------------`


`\bf \cfrac{21x^2y^6+6xy^3-30xy}{3xy}\implies \stackrel{\textit{distributing the denominator}}{\cfrac{21x^2y^6}{3xy}+\cfrac{6xy^3}{3xy}-\cfrac{30xy}{3xy}} \\\\\\ \cfrac{21}{3}\cdot x^2x^(-1)y^6y^(-1)+\cfrac{6}{3}\cdot x^1x^(-1)y^3y^(-1)-\cfrac{30}{3}\cdot x^1x^(-1)y^1y^(-1) \\\\\\ 7x^(2-1)y^(6-1)+2x^(1-1)y^(3-1)-10x^(1-1)y^(1-1)\implies 7xy^5+2y^2-10`