Problem: If n♡m=n3m2n\heartsuit m=n^3m^2n♡m=n3m2, what is 2♡44♡2\dfrac{2\heartsuit 4}{4\heartsuit 2}4♡22♡4?
Answer Choices:
A. 14\dfrac{1}{4}41
B. 12\dfrac{1}{2}21
C. 111
D. 222
E. 444
Solution:
2♡44♡2=23⋅4243⋅22=24=(B)12\dfrac{2 \heartsuit 4}{4 \heartsuit 2}=\dfrac{2^{3} \cdot 4^{2}}{4^{3} \cdot 2^{2}}=\dfrac{2}{4}= (\text{B})\boxed{\dfrac{1}{2}} 4♡22♡4=43⋅2223⋅42=42=(B)21
The problems on this page are the property of the MAA's American Mathematics Competitions