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

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Math Expert
Joined: 02 Sep 2009
Posts: 50586
If a and b are positive integers and (2^a)^b = 2^3, what is the value  [#permalink]

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03 Jul 2016, 10:39
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77% (01:05) correct 23% (01:08) wrong based on 637 sessions

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

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03 Jul 2016, 11:46
2
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 = 23
=>2^ab = 23
2 raised to any integer power can't be an odd number .
Hi Bunuel
i think it should be (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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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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03 Jul 2016, 23:21
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
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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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04 Jul 2016, 08:13
(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.
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Joined: 13 Jan 2016
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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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04 Jul 2016, 08:30
1
ab=3. 3+1=4. Hence, the answer is 2^4= 16
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Joined: 26 Apr 2016
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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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08 Jul 2016, 10:44
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:
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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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14 Apr 2017, 00:35
1
1
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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Re: If a and b are positive integers and (2^a)^b = 2^3, what is the value  [#permalink]

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14 Jul 2018, 07:43
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Re: If a and b are positive integers and (2^a)^b = 2^3, what is the value &nbs [#permalink] 14 Jul 2018, 07:43
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