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) 5â‹…6
(B) 6â‹…6â‹…6â‹…5
(C) 5â‹…5â‹…5â‹…6
(D) 5â‹…5â‹…6
(E) 6â‹…6â‹…5
and note that (B) is largest.