Question: Simplify.
$$(5x^2y^4)^3$$
=
1. **State the problem:** Simplify the expression $$(5x^2y^4)^3$$.
2. **Recall the power of a product rule:** $$(abc)^n = a^n b^n c^n$$.
3. **Apply the rule:**
$$ (5x^2y^4)^3 = 5^3 \cdot (x^2)^3 \cdot (y^4)^3 $$
4. **Simplify each term:**
$$ 5^3 = 125 $$
$$ (x^2)^3 = x^{2 \times 3} = x^6 $$
$$ (y^4)^3 = y^{4 \times 3} = y^{12} $$
5. **Combine all:**
$$ 125 x^6 y^{12} $$
**Final answer:**
$$ \boxed{125 x^6 y^{12}} $$