Final answer:
The simplified form of the expression 3x⁴³³ is 27x¹².
Step-by-step explanation:
The simplified form of the expression 3x⁴³³ is 27x12 (option D).
To simplify the expression, we need to multiply the exponent outside the parentheses with the exponents inside the parentheses. In this case, we have 3 raised to the power of 4 raised to the power of 33, which can be written as (34)33. By using the power rule of exponents, we can multiply the exponents, so 34*33 = 3132.
Then, we simplify further by recognizing that 3132 can be written as (34)33 which is equal to 2733. Finally, we can rewrite 2733 as (33)33 = 33*33 = 399.
Therefore, the simplified form of the expression 3x⁴³³ is 27x12 (option D).