Final answer:
The answer to one-third of 3⁶, considering the properties of exponents and when taking the cube root, is 3².
Step-by-step explanation:
The original question asks, What is one-third of 3⁶? The answer is 3³.
To solve this, you need to understand the properties of exponents. If you have a power like 3⁶, and you want to find one-third of that power, you essentially divide the exponent by 3. Thus, one-third of 3⁶ is 3^(6/3) which simplifies to 3², which is not one of the options provided. However, if we interpret "one-third of 3⁶" as taking the cube root (or the one-third power) of 3⁶, the calculation would be (3⁶)^(1/3), which is 3^(6*1/3) = 3². Therefore, the correct answer is 3², not 3³ as provided in the original question.