SAT Question c6e85cd7: Equivalent Expressions answer and explanation with Desmos solution

An expression of the form $\sqrt[n]{a^m}$, where $m$ and $n$ are integers greater than $1$ and $a\ge 0$, is equivalent to $a^{\frac{m}{n}}$. Therefore, the expression on the right-hand side of the given equation, $\sqrt[3]{4^7}$, is equivalent to $4^{\frac{7}{3}}$. Thus, $4^{8c}=4^{\frac{7}{3}}$. It follows that $8c=\frac{7}{3}$. Dividing both sides of this equation by $8$ yields $c=\frac{7}{24}$. Note that 7/24, .2916, .2917, 0.291, and 0.292 are examples of ways to enter a correct answer.