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avatar+144 

Without using a calculator, order the following numbers from least to greatest:

\(A= \frac{2^{1/2}}{4^{1/6}}\\ B= \sqrt[12]{128}\vphantom{dfrac{2}{2}}\\ C= \left( \frac{1}{8^{1/5}} \right)^2\\ \)

\(D= \sqrt{\frac{4^{-1}}{2^{-1} \cdot 8^{-1}}}\\\)

\(E= \sqrt[3]{2^{1/2} *4^{-1/4}}\)
Give your answer as a list of capital letters separated by commas. For example, if you think that , then you would answer E,B,C,D,A.

 Oct 8, 2018
 #1
avatar+99523 
+1

Put everything in terms of powers on 2

 

A  =  2^(1/2)  / 4^(1/6)  =  2^(1/2)  / (2^2)^(1/6)  = 2^(1/2) / 2^(2/6)  = 2^(3/6) / 2^(2/6)  =

2^(1/6)  = 2^(2/12)

 

B   =   (128)^(1/12)  =   (2^7)^(1/12)  = 2^(7/12)

 

C =  [ 8^(-1/5)] ^2  =  [ (2^3)^(-1/5) ]^2  = [ 2^(-3/5) ]^2  = 2^(-6/5)

 

D  =  √  [  (2)^1 * 8^(1) /   4^(1) ]  =  √  [16 / 4 ]  = √ 4  =  2  = 2^(1)

 

E   =  [ 2^(1/2)  *  (2^2)^(-1/4) ] ^(1/3)  = [ 2^(1/2) * 2^(-2/4) ]^(1/3)  =

[ 2^(1/2) * 2^(-1/2) ]^(1/3)  = [ 2^0]^(1/3)  = 2^0

 

So..in order, we have

 

2^(-6/5) < 2^(0) < 2^(2/12) < 2^(7/12) < 2^(1)

 

So

 

C   E   A   B   D

 

 

cool cool cool

 Oct 8, 2018
 #2
avatar+144 
+1

Thankyou!

HelpPLZ  Oct 8, 2018
 #3
avatar+10252 
+2

Without using a calculator, order the following numbers from least to greatest:

 

 Oct 8, 2018

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