SAT Question 1be909aa: Equivalent Expressions answer and explanation with Desmos solution

Choice A is correct. For positive values of $a$, $\frac{a^m}{a^n}=a^{\left(m-n\right)}$, where $m$ and $n$ are integers. Since it's given that $h>0$ and $q>0$, this property can be applied to rewrite the given expression as $\left(h^{\left(15-5\right)}\right)\left(q^{\left(7-21\right)}\right)$, which is equivalent to $h^{10}{q}^{-14}$. For positive values of $a$, $a^{-n}=\frac{1}{a^n}$. This property can be applied to rewrite the expression $h^{10}{q}^{-14}$ as $\left(h^{10}\right)\left(\frac{1}{q^{14}}\right)$, which is equivalent to $\frac{h^{10}}{q^{14}}$.