1. **Problem Statement:** Simplify the expression $9x^5 y^2 x - 2x^{-2} y^{-2}$. 2. **Recall the laws of exponents:** - $x^a \cdot x^b = x^{a+b}$ - $x^{-a} = \frac{1}{x^a}$ 3. **Simplify each term:** - $9x^5 y^2 x = 9x^{5+1} y^2 = 9x^6 y^2$ - $-2x^{-2} y^{-2} = -2 \frac{1}{x^2} \frac{1}{y^2} = -\frac{2}{x^2 y^2}$ 4. **Final simplified expression:** $$9x^6 y^2 - \frac{2}{x^2 y^2}$$ This is the simplified form combining the positive and negative powers.