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

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Bunuel
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If the operation a* is defined by a* = 1/(a^3)^(1/2) what is the value [#permalink] New post   03 Jun 2020, 09:50
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E

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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
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Re: If the operation a* is defined by a* = 1/(a^3)^(1/2) what is the value [#permalink] New post   03 Jun 2020, 10:02
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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
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Re: If the operation a* is defined by a* = 1/(a^3)^(1/2) what is the value [#permalink] New post   05 Jun 2020, 18:15
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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
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Re: If the operation a* is defined by a* = 1/(a^3)^(1/2) what is the value [#permalink] New post   06 Jun 2020, 17:18
IMO answer is E
Unfortunately I can’t show the process it’s all under a big sqrt(within sqrt())

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Re: If the operation a* is defined by a* = 1/(a^3)^(1/2) what is the value [#permalink]
06 Jun 2020, 17:18
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