Problem:
Which of these numbers is largest?
Answer Choices:
A. 35⋅6
B. 635
C. 536
D. 356
E. 365
Solution:
If a and b are positive, then a<b if and only if a6<b6. Since all the choices are positive, raise each to the sixth power to simplify the comparison:
(A) 5⋅6
(B) 6⋅6⋅6⋅5
(C) 5⋅5⋅5⋅6
(D) 5⋅5⋅6
(E) 6⋅6⋅5
and note that (B) is largest.