1. **State the problem:** Verify if the simplification of question 11 is correct. Given expression: $$\frac{(2m^2)^{-1}}{m^2}$$ 2. **Recall the rules:** - Negative exponent rule: $$a^{-n} = \frac{1}{a^n}$$ - Power of a product: $$(ab)^n = a^n b^n$$ - Division of same bases: $$\frac{a^m}{a^n} = a^{m-n}$$ 3. **Simplify numerator:** $$(2m^2)^{-1} = 2^{-1} \cdot (m^2)^{-1} = \frac{1}{2} \cdot m^{-2} = \frac{m^{-2}}{2}$$ 4. **Rewrite the entire expression:** $$\frac{(2m^2)^{-1}}{m^2} = \frac{\frac{m^{-2}}{2}}{m^2} = \frac{m^{-2}}{2} \cdot \frac{1}{m^2} = \frac{m^{-2}}{2m^2}$$ 5. **Combine powers of $m$ in the denominator:** $$2m^2 = 2 \cdot m^2$$ 6. **Simplify powers of $m$:** $$\frac{m^{-2}}{m^2} = m^{-2 - 2} = m^{-4}$$ 7. **Final expression:** $$\frac{m^{-2}}{2m^2} = \frac{1}{2} m^{-4} = \frac{1}{2m^4}$$ 8. **Compare with user's answer:** User's answer is $$-2 m^{-4}$$ but the correct answer is $$\frac{1}{2} m^{-4}$$. **Conclusion:** The user's answer is incorrect because the coefficient and sign are wrong.