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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.

 Jan 3, 2021
 #1
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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.

 Jan 3, 2021

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