Final answer:
The simplified form of the expression (3x^4)^3 is 27x^12, where 3 is cubed to get 27 and the exponent 4 is multiplied by 3 to get x^12.
Step-by-step explanation:
The simplified form of the expression (3x^4)^3 is obtained through cubing both the coefficient and the variable separately. When cubing the coefficient 3, we get 3^3 which equals 27. For the variable part, we apply the rule of multiplying exponents when raising a power to a power. Hence, x^4 raised to the 3rd power becomes x^(4*3) which is x^12. Therefore, the simplified expression is 27x^12.