I am trying to show algebraically that $8^3>9^{8/3}$. This came from trying to complete the base case of an induction proof.
I have struggled because $8$ and $9$ cannot be manipulated to be the same base. Otherwise I could just argue that $3>\dfrac{8}{3}$.
I tried raising both sides to the third power and got $8^9>9^8$. I can rewrite this as $8^9>9^{9-1}$ but I am not sure if this is the right direction.