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What is the simplified form of the expression (3x^4)3?

A. 9x^7
B. 9x^12
C. 27x^7
D. 27x^12

1 Answer

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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.

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