Arrange the following numbers in decreasing order: 2^5555, 3^3333, 6^2222

Question

You are given with six numbers – 1, 2, 3, 4, 5 and 6. You can arrange them in any order and you can use all four mathematics expressions i.e. add, subtract, multiply and divide and also parenthesis. The result must be 278.

There are three other rules
1) You can only use a number once.
2) It is not compulsory to use all the six numbers.
3) You can’t join numbers i.e. you can’t use 1, 2 and 3 as 123.

Answer 1

6^2222 > 2^5555 > 3^3333

Logic
do it for low number ie 6^2, 2^5 and 3^3 which is 36, 32 and 27 hence the answer.

Answer 2

5555 log 2= 1111 log 2^5= 1111 log 32
3333 log 3=1111 log 3^3 = 1111 log 27
2222 log 6= 1111 log 6^2= 1111 log 36

Since log 36>log 32>log 27
Therefore 6^2222 > 2^5555 > 3^3333