1. **Stating the problem:** Simplify the expression $x(12y^2 + 16)x(12y^2 + 16)x(12y^2 + 16)$. 2. **Rewrite the expression:** Notice that the expression is $x(12y^2 + 16)$ multiplied by itself three times, so it can be written as \[\left(x(12y^2 + 16)\right)^3.\] 3. **Simplify inside the parentheses:** The term inside the parentheses is $x(12y^2 + 16)$. We can leave it as is for now. 4. **Express the cube:** \[\left(x(12y^2 + 16)\right)^3 = x^3 (12y^2 + 16)^3.\] 5. **Factor the constant inside the parentheses:** \[12y^2 + 16 = 4(3y^2 + 4).\] 6. **Rewrite the expression:** \[x^3 (4(3y^2 + 4))^3 = x^3 4^3 (3y^2 + 4)^3 = x^3 64 (3y^2 + 4)^3.\] 7. **Final simplified form:** \[64 x^3 (3y^2 + 4)^3.\] This is the fully simplified expression.