Problem:
Suppose that P=2m and Q=3n. Which of the following is equal to 12mn for every pair of integers (m,n)?
Answer Choices:
A. P2Q
B. PnQm
C. PnQ2m
D. P2mQn
E. P^{2 n} Q^
Solution:
Note that
12mn=(22⋅3)mn=22mn⋅3mn=(2m)2n⋅(3n)m=(E)P2nQm​
Remark: The pair of integers (2,1) shows that the other choices are not possible.
The problems on this page are the property of the MAA's American Mathematics Competitions