What's the best method for solving these without a graph.
Find $\displaystyle \left\{ x:x^{\frac{3}{2}}>x^2 \right\}$
It should be clear to you that $\displaystyle x\ge 0$ else $\displaystyle x^{\frac{3}{2}}$ is not defined.
Therefore $\displaystyle x^3>x^4$.
Now go for it.