Given:

• pp is of the form 3n3^n, i.e., p=3np = 3^n
• qq is of the form 6n×5m6^n \times 5^m, i.e., q=6n×5mq = 6^n \times 5^m

where mm and nn are non-negative integers.

Analyzing the Forms of pp and qq

1. Factorizing qq:
   Since 6n=(2×3)n=2n×3n6^n = (2 \times 3)^n = 2^n \times 3^n, we can rewrite qq as:

   q=(2n×3n)×5m=2n×3n×5mq = (2^n \times 3^n) \times 5^m = 2^n \times 3^n \times 5^m

2. Comparing Powers of Prime Factors
   • pp contains only powers of 3.
   • qq contains powers of 2, 3, and 5.

Observations

• If pp and qq are to be compared or related, qq contains an extra factor of 2n2^n and 5m5^m compared to pp.
• pp can divide qq only when 2n×5m=12^n \times 5^m = 1, which is possible only when n=0n = 0 and m=0m = 0.
• In general, pp and qq may not always have a simple multiple or factor relationship unless additional constraints are given.