1. **State the problem:** Simplify the expression $$(5p^2)^2(2p)^2$$ and find which of the given options matches the simplified form. 2. **Recall the exponent rules:** - When raising a power to another power, multiply the exponents: $$(a^m)^n = a^{mn}$$ - When multiplying terms with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 3. **Simplify each part:** - Simplify $$(5p^2)^2$$: $$ (5p^2)^2 = 5^2 \cdot (p^2)^2 = 25p^{2 \times 2} = 25p^4 $$ - Simplify $$(2p)^2$$: $$ (2p)^2 = 2^2 \cdot p^2 = 4p^2 $$ 4. **Multiply the simplified parts:** $$ 25p^4 \cdot 4p^2 = (25 \cdot 4)(p^4 \cdot p^2) = 100p^{4+2} = 100p^6 $$ 5. **Final answer:** $$\boxed{100p^6}$$ matches the third option.