If the operation a* is defined by a* = 1/(a^3)^(1/2) what is the value

Question

If the operation a* is defined by  a* = \frac{1}{\sqrt{a^3}}  what is the value of  (2^{-\frac{1}{4*}})*

A.  -2^{-\frac{1}{12}}

B.  -2^{12}

C.  2^{-12}

D.  2^{\frac{3}{16}}

E.  2^{12}

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NitishJain · Answer

IMO  E

Given a* = a∗=1/sqrt (a^3) = a ^ (-3/2). --eq 1

4* = 4^(-3/2) = 2^ (2* {-3/2}) = 2^(-3) = 1/8

Putting this value we get: 2 ^ (-1 * 1/8 ) *= 2 ^(-8) *

From eqn 1: 2 ^ (-8 * -3/2) = 2^12

KhulanE · Answer

4*=1/sqrt(4^3)=1/sqrt(2^(2/3))=1/(2^3)=1/8
-1/4*=-1/(1/8)=-8
(2^(-1/4*))*=(2^-8)*=1/sqrt((2^-8)^3)=1/sqrt(2^-24)=1/2^-12=2^12
E is the answer

Babineaux · Answer

IMO answer is E 
Unfortunately I can’t show the process it’s all under a big sqrt(within sqrt())

Posted from my mobile device

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=KjP5FpHUhds

a* = \frac{1}{\sqrt{a^3}}  and we need to find the value of  (2^{-\frac{1}{4*}})*

a* = \frac{1}{\sqrt{a^3}}  =  1/a^{3/2}  =  a^{-3/2}

Lets start by finding the value of 4*

=> We need to substitute a with 4 in  a* = a^{-3/2}  to get the value of 4*

4* = 4^{(-3/2)}  = (2^2)^(-3/2) = 2^(2*-3/2) = 2^-3

=>   (2^{-\frac{1}{4*}})*  =  (2^{-\frac{1}{2^{-3}}})*  =  (2^{-2^3})*  =  (2^{-8})*

(2^{-8})* = (2^{-8})^{(-3/2)}  =  2^{12}

So,  Answer will be E 
Hope it helps!

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https://www.youtube.com/watch?v=b7JoMX0gk8M

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