1. The problem is to simplify the expression $9m^{\frac{2}{3}} - 5m^{\frac{3}{4}}$. 2. This expression involves subtracting two terms with different fractional exponents on the variable $m$. 3. Since the exponents $\frac{2}{3}$ and $\frac{3}{4}$ are different, and the bases are the same, these terms cannot be combined by addition or subtraction. 4. Therefore, the simplified form of the expression is simply the expression itself: $$9m^{\frac{2}{3}} - 5m^{\frac{3}{4}}$$ 5. No further simplification is possible unless additional information about $m$ is given.