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

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Math Expert
Joined: 02 Sep 2009
Posts: 58371
If 2^a = b then 8^a must equal to  [#permalink]

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29 Dec 2014, 09:08
00:00

Difficulty:

5% (low)

Question Stats:

79% (00:56) correct 21% (01:21) wrong based on 212 sessions

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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.

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

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29 Dec 2014, 09:21
3
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

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

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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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30 Dec 2014, 19:45
1

$$2^a = b$$

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

$$2^{3a} = b^3$$

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

$$8^a = b^3$$
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Joined: 21 Dec 2014
Posts: 9
Re: If 2^a = b then 8^a must equal to  [#permalink]

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01 Jan 2015, 19:17
1
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.
Intern
Joined: 09 Apr 2013
Posts: 31
Schools: Booth '16
Re: If 2^a = b then 8^a must equal to  [#permalink]

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04 Jan 2015, 11:19
1
2^a = b

apply 3rd power on both sides => (2^a)^3 = b^3
=> (2^3)^a = b^3
=> 8^a = b^3
Math Expert
Joined: 02 Sep 2009
Posts: 58371
Re: If 2^a = b then 8^a must equal to  [#permalink]

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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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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.

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

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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

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

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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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