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If 2^a = b then 8^a must equal to

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If 2^a = b then 8^a must equal to [#permalink]

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New post 29 Dec 2014, 09:08
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Re: If 2^a = b then 8^a must equal to [#permalink]

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I would pick simple numbers to solve this. Say a = 2, then b = 2^2 = 4, so 8^2 = 64. Check the solutions:

A. b^3 = 4^3 = 64, which is what we're looking for.
B. b^2 = 16, not correct
C. 3b = 12, not correct
D. b^(2a) = 256, not correct
E. b^(3a) = 4096, not correct

Answer is A.
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Re: If 2^a = b then 8^a must equal to [#permalink]

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New post 30 Dec 2014, 11:09
Bunuel wrote:

Tough and Tricky questions: Exponents.



If 2^a = b then 8^a must equal to

A. b^3
B. b^2
C. 3b
D. b^(2a)
E. b^(3a)

Kudos for a correct solution.



2^a = b

8^a = 2^3a = 2^(a*3) = b^3

Ans A
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Re: If 2^a = b then 8^a must equal to [#permalink]

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New post 30 Dec 2014, 19:45
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Answer = A. b^3

\(2^a = b\)

\((2^a)^3 = b^3\)

\(2^{3a} = b^3\)

\((2^3)^a = b^3\)

\(8^a = b^3\)
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Re: If 2^a = b then 8^a must equal to [#permalink]

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Best approach in such queries is to look for each answers, we know we cannot substitute the value of a in 8^a from 2^a = b.
So , we go to answers straight.
look for options- A says b^3 which is 2^a ^3 = 8^a.
So in this case we dont look further and go to the right answer which option A.

When questions and answers both are in variable in PS, subtituting with numbers such as 2/3, may not be a quick idea.

Bunuel wrote:

Tough and Tricky questions: Exponents.



If 2^a = b then 8^a must equal to

A. b^3
B. b^2
C. 3b
D. b^(2a)
E. b^(3a)

Kudos for a correct solution.
1 KUDOS received
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Re: If 2^a = b then 8^a must equal to [#permalink]

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New post 04 Jan 2015, 11:19
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2^a = b

apply 3rd power on both sides => (2^a)^3 = b^3
=> (2^3)^a = b^3
=> 8^a = b^3
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Re: If 2^a = b then 8^a must equal to [#permalink]

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New post 08 Jan 2015, 09:43
Bunuel wrote:

Tough and Tricky questions: Exponents.



If 2^a = b then 8^a must equal to

A. b^3
B. b^2
C. 3b
D. b^(2a)
E. b^(3a)

Kudos for a correct solution.


OFFICIAL SOLUTION:

(A) 8ª = (2³)ª = 2³ª = (2ª)³

Since 2ª = b then (2ª)³ = b³, choice (A).
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Re: If 2^a = b then 8^a must equal to [#permalink]

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New post 22 Sep 2017, 07:26
Quote:

If 2^a = b then 8^a must equal to

A. b^3
B. b^2
C. 3b
D. b^(2a)
E. b^(3a)


Since 8^a = (2^3)^a = (2^a)^3 and 2^a = b, 8^a = b^3.

Answer: A
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Re: If 2^a = b then 8^a must equal to [#permalink]

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New post 20 Mar 2018, 16:27
Bunuel wrote:

Tough and Tricky questions: Exponents.



If 2^a = b then 8^a must equal to

A. b^3
B. b^2
C. 3b
D. b^(2a)
E. b^(3a)

Kudos for a correct solution.


Let a =2...then 2^2 = 4

8^a = 8^2 =64 = 4^3 = b^3

Answer: A
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Re: If 2^a = b then 8^a must equal to [#permalink]

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New post 21 Mar 2018, 04:56
Bunuel wrote:

Tough and Tricky questions: Exponents.



If 2^a = b then 8^a must equal to

A. b^3
B. b^2
C. 3b
D. b^(2a)
E. b^(3a)

Kudos for a correct solution.


\(2^a = b ------(I)\)

\(8^a\)

\((2^3)^a\)

\((2^a)^3\)

Replace \(2^a\) with "b" as per equation (I)

\(b^3\)

(A)
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Re: If 2^a = b then 8^a must equal to   [#permalink] 21 Mar 2018, 04:56
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