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If 4^a*4^b=2(8^3), what is the value of a+b?

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Carcass
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If 4^a*4^b=2(8^3), what is the value of a+b? [#permalink] New post   21 Feb 2021, 10:51
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If \(4^a*4^b=2(8^3)\), what is the value of a+b?

A. 4
B. 5
C. 6
D. 7
E. 8


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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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B
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If 4^a*4^b=2(8^3), what is the value of a+b? [#permalink] New post   21 Feb 2021, 11:14
Solution:

\(4^a*4^b=2^2^a*2^2^b\)
\(2(8^3)=2(2^3^*^3)=2(2^9)=2^1^0\)

\(2^2^a*2^2^b=2^1^0\)
2a+2b=10
Dividing throughout by 2
a+b=5

IMO B

Hope this helps!
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If 4^a*4^b=2(8^3), what is the value of a+b? [#permalink] New post   21 Feb 2021, 11:50
Carcass wrote:
If \(4^a*4^b=2(8^3)\), what is the value of a+b?

A. 4
B. 5
C. 6
D. 7
E. 8


\(4^a*4^b = 2*(8^3)\)

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

\(2^{2a+2b} = 2^{10}\)

When the bases are equal, the powers are equal

\(2a + 2b = 10\)

\(a + b = 5\)

Hence, option B
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Re: If 4^a*4^b=2(8^3), what is the value of a+b? [#permalink] New post   21 Feb 2021, 12:03
Carcass wrote:
If \(4^a*4^b=2(8^3)\), what is the value of a+b?

A. 4
B. 5
C. 6
D. 7
E. 8


Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book


Let's rewrite all terms with the same base, and let's make 2 the common base.
Given: 4^a x 4^b = 2(8^3)
Rewrite 4 and 8 as powers of 2: (2^2)^a x (2^2)^b = 2((2^3)^3)
Simplify: 2^(2a) x 2^(2b) = (2)(2^9)
Simplify again: 2^(2a + 2b) = 2^10
Since the bases are now equal, we can conclude that 2a + 2b = 10
Divide both sides by 2 to get: a + b = 5

Answer: B
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Re: If 4^a*4^b=2(8^3), what is the value of a+b? [#permalink] New post   27 Apr 2021, 03:58
In this case, I do not see the advantage of distributing the 2 into (a+b) since the question is asking what that quantity is. We can consider it a single variable in this case, right?

After making the same base to equate the exponents, ended with

2(a+b)=10

.

Same answer in the end, but eliminating a potential place for error.
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Re: If 4^a*4^b=2(8^3), what is the value of a+b? [#permalink] New post   28 Apr 2021, 05:19
2(a+b)=10
a+b=5
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Re: If 4^a*4^b=2(8^3), what is the value of a+b? [#permalink]
28 Apr 2021, 05:19
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