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

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New post 03 Jul 2016, 10:39
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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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New post 03 Jul 2016, 11:46
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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 = 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
Answer C
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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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New post 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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Re: If a and b are positive integers and (2^a)^b = 2^3, what is the value  [#permalink]

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

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New post 04 Jul 2016, 08:30
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ab=3. 3+1=4. Hence, the answer is 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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New post 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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New post 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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New post 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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