Final answer:
The expression equivalent to (3²)⁶ is C. 3¹² because when you raise a power to another power, you multiply the exponents, resulting in 3 raised to the exponent of 12 (or 3¹²).
Step-by-step explanation:
The question is asking for expressions that are equivalent to (3²)⁶. To find the equivalent expressions, we must apply the rules of exponents, particularly the power of a power rule, which states that when raising an exponent to another power, you multiply the exponents. In this case, option c is the correct answer 3¹², which is 3 raised to the 12th power.
Therefore, the expressions equivalent to (3²)⁶ would be those that are also equal to 3¹. Reviewing each option:
- A. 1/3¹² is not equivalent, as it is the reciprocal of 3¹².
- B. 3⁸ is not equivalent, because 8 is not equal to 12.
- C. 3¹² is equivalent, as it is precisely the expanded form of (3²)⁶.
- D. 1/3⁸ is not equivalent for the same reason as A; it's a reciprocal, and 8 is not 12.
The correct answer is C. 3¹².