Final answer:
The greatest common divisor of 6³ and 3¶ is 3³, or 27, found by comparing the prime factors of both numbers and selecting the common base with the smallest exponent.
Step-by-step explanation:
The greatest common divisor (GCD) of the numbers 6³ (6 cubed) and 3¶ (3 to the sixth power) can be found by breaking down the numbers into their prime factors. The number 6³ can be expressed as (2 * 3)³, which simplifies to 2³ * 3³. Similarly, 3¶ is simply 3¶. To find the GCD, we look for the highest exponent of the common base that appears in both factorizations. In this case, the common base is 3, with an exponent of 3 in 6³ and an exponent of 6 in 3¶, so the GCD is 3³.
Therefore, the greatest common divisor of 6³ and 3¶ is 3³, which is 27.