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# What is the value of 4^(a + b)/2^(a - b) ?

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
What is the value of 4^(a + b)/2^(a - b) ?  [#permalink]

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12 Sep 2017, 22:33
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Difficulty:

45% (medium)

Question Stats:

63% (01:07) correct 37% (01:23) wrong based on 106 sessions

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What is the value of $$\frac{4^{(a + b)}}{2^{(a - b)}}$$ ?

(1) a = 7
(2) a + 3b = 5

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Joined: 31 Jan 2017
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Re: What is the value of 4^(a + b)/2^(a - b) ?  [#permalink]

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12 Sep 2017, 22:40
on simplifying the equation we 2^a+3b

S1: a=7 insuff
b could be 2,3,4 .....
S2: a+3b=5
2^5=32 Suff..
Ans B
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What is the value of 4^(a + b)/2^(a - b) ?  [#permalink]

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12 Sep 2017, 23:16
1
The expression for which the value has to be found can be simplified as follows:

$$\frac{4^{(a + b)}}{2^{(a - b)}}$$ $$= \frac{2^{2(a + b)}}{2^{(a - b)}}$$ $$= \frac{2^{(2a + 2b)}}{2^{(a - b)}}$$ = $$2^{2a + 2b - a + b} = 2^{a + 3b}$$

(1) a = 7
Just knowing the value of a,
we cannot find the value of the expression(Insufficient)

(2) a + 3b = 5
Since we have simplified the expression as $$2^{a + 3b}$$
knowing the value of$$a + 3b$$ is enough
to find the value of the expression (Sufficient) (Option B)
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Re: What is the value of 4^(a + b)/2^(a - b) ?  [#permalink]

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16 Oct 2018, 23:14
4^(a+b)/2^(a-b)

Use the property X^m/X^n = X^m-n and simply the equation

After simplifying, you will get 2^a+3b

From this we can conclude that B is the answer

St1: No information about b. Hence we can get multiple values - Insufficient AD/BCE
St2: a+3b = 5. Plug 5 into the simplified equation and you will get a definite answer 2^5. - Sufficient - AD/BCE
Re: What is the value of 4^(a + b)/2^(a - b) ?   [#permalink] 16 Oct 2018, 23:14
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