SAT Question d9137a84: Equivalent Expressions answer and explanation with Desmos solution

Choice D is correct. The product of $\left(x^{-6}{y}^3{z}^5\right)$ and $\left(x^4{z}^5+y^8{z}^{-7}\right)$ can be represented by the expression $\left(x^{-6}{y}^3{z}^5\right)\left(x^4{z}^5+y^8{z}^{-7}\right)$. Applying the distributive property to this expression yields $\left(x^{-6}{y}^3{z}^5\right)\left(x^4{z}^5\right)+\left(x^{-6}{y}^3{z}^5\right)\left(y^8{z}^{-7}\right)$, or $x^{-6}{x}^4{y}^3{z}^5{z}^5+x^{-6}{y}^3{y}^8{z}^5{z}^{-7}$. This expression is equivalent to $x^{-6+4}{y}^3{z}^{5+5}+x^{-6}{y}^{3+8}{z}^{5-7}$, or $x^{-2}{y}^3{z}^{10}+x^{-6}{y}^{11}{z}^{-2}$.