1. **State the problem:** Simplify the expression $$(2^2 y^5)^{-2}$$. 2. **Recall the exponent rules:** - Power of a power: $$(a^m)^n = a^{m \times n}$$ - Negative exponent: $$a^{-n} = \frac{1}{a^n}$$ - Power of a product: $$(ab)^n = a^n b^n$$ 3. **Apply the power of a product rule:** $$(2^2 y^5)^{-2} = (2^2)^{-2} (y^5)^{-2}$$ 4. **Simplify each part:** $$(2^2)^{-2} = 2^{2 \times (-2)} = 2^{-4}$$ $$(y^5)^{-2} = y^{5 \times (-2)} = y^{-10}$$ 5. **Rewrite with negative exponents as fractions:** $$2^{-4} = \frac{1}{2^4} = \frac{1}{16}$$ $$y^{-10} = \frac{1}{y^{10}}$$ 6. **Combine the results:** $$\frac{1}{16} \times \frac{1}{y^{10}} = \frac{1}{16 y^{10}}$$ **Final answer:** $$\boxed{\frac{1}{16 y^{10}}}$$ This matches answer choice A (and also E, which is the same).