+0  
 
0
130
12
avatar+416 

Ive been wondering about this one I think its pretty good! 

 

Arrange the following numbers in increasing order:

\(\begin{align*} A &= \frac{2^{1/2}}{4^{1/6}}\\ B &= \sqrt[12]{128}\vphantom{dfrac{2}{2}}\\ C &= \left( \frac{1}{8^{1/5}} \right)^2\\ D &= \sqrt{\frac{4^{-1}}{2^{-1} \cdot 8^{-1}}}\\ E &= \sqrt[3]{2^{1/2} \cdot 4^{-1/4}}.\vphantom{dfrac{2}{2}} \end{align*}\)
Enter the letters, separated by commas. For example, if you think that D

 

Could you guys take a look? Ty!

 Mar 23, 2020
 #1
avatar+111321 
+1

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

 

B    (128)^(1/28)  = [ 2^(7)]^(1/28)  = 2^(1/4)

 

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

 

D     Note    4^(-1)  = 1/4       2^(-1)  = 1/2    8^(-1)  = 1/8

 

So  what  we have inside the radical is just this :

 

                1/4                        1/4

             _________   =    _______   =   (1/4) * (16/1)   =   4

              1/2  * 1/8                1/16  

 

And       the sqrt of this =   2

 

E     Inside  the radical  we have 

 

2^(1/2) * 4^(-1/4)  =

 

2^(1/2) * (2^2)^(-1/4)   =

 

2^(1/2) * 2^(-1/2)  =

 

2^(1/2 - 1/2) =

 

2^0  = 

 

1

 

And the cube root of this   is still   just 1

 

So  in order we have

 

2^(-3/5) ,  2^(1/6)  ,  2^(1/4) , 1 , 2

 

C , A , B , E , D

 

 

cool cool cool

 Mar 23, 2020
 #2
avatar+2854 
+1

lol I just plugged the values into the web 2.0 calculator cuz i'm lazy

CalculatorUser  Mar 23, 2020
 #3
avatar+416 
+2

Hmm Im still confused! I think we did it wrong somewhere! Caculator user was CPhill right? :) Lol

 Mar 23, 2020
 #4
avatar+2854 
+1

I'm not CPhill. Our age difference measures in multiple decades XD trololololololol

CalculatorUser  Mar 23, 2020
 #5
avatar+416 
+2

Aww dont be a bully

 Mar 23, 2020
 #6
avatar+416 
+2

When your so bored that you have a compition between two leaderboard people. Lol its like 9 o clock here.

 Mar 23, 2020
 #7
avatar+2854 
+1

its 11 pm here. I've become semi-nocturnal since my school shutdown :/

CalculatorUser  Mar 23, 2020
 #8
avatar+416 
+2

Lol same here I stay up until like 4 then wake up at like 10

 Mar 23, 2020
 #9
avatar+416 
+2

REET its time to grind math! I still dont think its right!!!!!

 Mar 23, 2020
 #10
avatar+2854 
+1

I stopped grinding math a few months ago cuz like im lazy

CalculatorUser  Mar 23, 2020
 #11
avatar+416 
+2

Lol

Same

But

I

Need

To 

Do

This

Maths

 Mar 23, 2020
 #12
avatar+2854 
0

i like making games on Scratch now and i work all day then start homework around 9-10

 

my math experience definitely helped!

CalculatorUser  Mar 23, 2020

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