Without using a calculator, order the following numbers from least to greatest:
A = 100^500
B = 200^400
C = 300^300
D = 400^200
E = 500^100
Give your answer as a list of capital letters separated by commas. For example, if you think that E < B < C < D < A, then you would answer E,B,C,D,A.
Try comparing them in pairs from the top down.
A = 100^500 = (100^400) * (100^100)
B = 200^400 = (100^400) * (2^400) = (100^400) * (16^100) < A
So B is less than A
B = (100^400) * (16^100) = (100^300) *(100^100) * (16^100) = (100^300) *(1600^100)
C = 300^300 = (100^300) * (3^300) = (100^300) * (27^100) < B
So C is less than B
And you can do the others.
It might be easier to compare them from the bottom up but it is still the same basic method.