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

Question

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

GMATinsight · Accepted Answer

Check answer explanation as mentioned below

Answer: option B

BrentGMATPrepNow · Answer

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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JeffTargetTestPrep · Answer

The key to solving this problem is to obtain the same base for the expressions in the equation. We notice that 4 = 2^2 and that 8 = 2^3; thus, the common base will be 2. Let’s simplify the given expression:

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

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

2^(2a + 2b) = 2^1(2^9)

2^(2a + 2b) = 2^10

2a + 2b = 10

a + b = 5

Answer: B

Abhishek009 · Answer

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

Or,  2^{2a}*2^{2b} =2(2^9)

Or,  2^{2a}*2^{2b} =2^{10}

Or,  2^{2a + 2b} = 2^{10}

So,  2a + 2b = 10

Or,  a + b = 5 , Answer must be (B)

Abhishek009 · Answer

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

Or,  2^{2a}*2^{2b}=2(2^9)

Or,  2^{2a+2b}=2^{10}

Or,  2a+2b=10

Or,  a+b=5 , Answer must be (B) 5

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

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

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