write these numbers in order from smallest to biggest show

write these numbers in order from smallest to biggest ( show your work )
2^ (1/2) , 3^(1/3) , 6^(1/6)

Solution

2^ (1/2) , 3^(1/3) , 6^(1/6)

raising each of the numbers to common exponent 6 it is the lowest common denominator for 2 and 3

--- 2^(1/2) = (2^(3/6) = (8)^1/6

---- 3^1/3 = 3^(2/6) = (9)^1/6

-----6^(1/6)

So, we can see from smallest is biggest 6^(1/6) , (2)^1/2 ,(3)^1/3