Answer:
7z^2/y -8z^4y -(9/2)z^2y^4
Step-by-step explanation:
The quotient of division of a polynomial by a monomial is the sum of quotients of each of the terms divided by the monomial. "Simplify" in this context generally means that no common factors remain factored out.
Rules of exponents
The rules of exponents apply:
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
Division
The problem is effectively three (3) division/simplification problems.
[tex]\dfrac{-14z^4y^2+16z^6y^4+9z^4y^7}{-2z^2y^3}=\dfrac{-14z^4y^2}{-2z^2y^3}+\dfrac{16z^6y^4}{-2z^2y^3}+\dfrac{9z^4y^7}{-2z^2y^3}\\\\=7z^{4-2}y^{2-3}-8z^{6-2}y^{4-3}-\dfrac{9}{2}z^{4-2}y^{7-3}=\boxed{\dfrac{7z^2}{y}-8z^4y-\dfrac{9}{2}z^2y^4}[/tex]
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Additional comment
We have elected to retain the original order of variables (z then y) and the original order of terms. Ordinarily, standard form would have the variables in alphabetical order (y then z) and the terms in order by decreasing degree. This order of terms also makes the leading coefficient positive. (The minus sign for a negative leading coefficient sometimes gets lost.)
