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Math Expert V
Joined: 02 Sep 2009
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If a and b are positive integers and (2^a)^b = 2^3, what is the value  [#permalink]

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Difficulty:   15% (low)

Question Stats: 76% (01:04) correct 24% (01:03) wrong based on 667 sessions

### HideShow timer Statistics If a and b are positive integers and $$(2^a)^b = 2^3$$, what is the value of $$2^a*2^b$$?

A) 6
B) 8
C) 16
D) 32
E) 64

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If a and b are positive integers and (2^a)^b = 2^3, what is the value  [#permalink]

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Bunuel wrote:
If a and b are positive integers and (2^a)^b = 23, what is the value of 2^a*2^b?

A) 6
B) 8
C) 16
D) 32
E) 64

(2^a)^b = 2^3
=>2^ab = 2^3
ab = 3
if a = 1 then b = 3 or if a=3 then b=1

2^a*2^b = 2^(a+b)
= 2^4 = 16
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Senior Manager  Joined: 02 Mar 2012
Posts: 284
Schools: Schulich '16
Re: If a and b are positive integers and (2^a)^b = 2^3, what is the value  [#permalink]

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c-16

ab=3.Since a and b are positive integers the only factors of prime number(this is the gist) 3 are 3 and 1.

so a can be 3 or 1 and b can also be 3 or 1

2^a+b=2^1+3 or 2^3+1=2^4=16
Intern  Joined: 06 Jul 2015
Posts: 20
Re: If a and b are positive integers and (2^a)^b = 2^3, what is the value  [#permalink]

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(2^a)^b = 2^ab
=> ab =3
and a and b are both integral values,
=> 3 can only be expressed as 1 * 3 as 3 is prime number
therefore a =1 and b =3 or b =1 and a =3
2^a * 2^b = 2^(a+b) = 2^(4) = 16.
Intern  B
Joined: 13 Jan 2016
Posts: 46
GMAT 1: 710 Q47 V40 Re: If a and b are positive integers and (2^a)^b = 2^3, what is the value  [#permalink]

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1
ab=3. 3+1=4. Hence, the answer is 2^4= 16
Intern  Joined: 26 Apr 2016
Posts: 8
Re: If a and b are positive integers and (2^a)^b = 2^3, what is the value  [#permalink]

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Bunuel wrote:
If a and b are positive integers and (2^a)^b = 2^3, what is the value of 2^a*2^b?

A) 6
B) 8
C) 16
D) 32
E) 64

Simple solution. Pick values of a and b, such that the given equation is true. Here, a could be 1 and b could be 3. (2^1)^3 = 2^3. With these values of a & b, the expression (2^a)(2^b) evaluates to be (2^1)(2^3) = 2 x 8 = 16. Answer choice:
Manager  S
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GMAT 1: 410 Q18 V27 GMAT 2: 490 Q35 V23 Re: If a and b are positive integers and (2^a)^b = 2^3, what is the value  [#permalink]

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1
2
Bunuel wrote:
If a and b are positive integers and (2^a)^b = 2^3, what is the value of 2^a*2^b?

A) 6
B) 8
C) 16
D) 32
E) 64

$${ \left( { 2 }^{ a } \right) }^{ b }={ 2 }^{ 3 }\\ { 2 }^{ ab }={ 2 }^{ 3 }\\ ab=3$$

ab must be $$(1)(3)$$ or $$(3)(1)$$

$${ 2 }^{ a }\ast { 2 }^{ b }={ 2 }^{ a+b }\\ { 2 }^{ 1+3 }={ 2 }^{ 4 }=16$$
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Non-Human User Joined: 09 Sep 2013
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Re: If a and b are positive integers and (2^a)^b = 2^3, what is the value  [#permalink]

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_________________ Re: If a and b are positive integers and (2^a)^b = 2^3, what is the value   [#permalink] 14 Jul 2018, 08:43
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