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Which of the following is equal to (2^k) ? A. 2(10^k 1) B.

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Which of the following is equal to (2^k) ? A. 2(10^k 1) B. [#permalink]

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New post 01 Oct 2008, 11:11
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Which of the following is equal to (2^k) [5^(k − 1)]?



A. 2(10^k − 1)
B. 5(10^k − 1)
C. 10^k
D. 2(10^k )
E. 10^2k − 1

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Re: Exponents [#permalink]

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New post 01 Oct 2008, 11:34
answer will be 10^k...

given eq = 2^5*5^k -2^k = 10^k -2^k

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Re: Exponents [#permalink]

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New post 01 Oct 2008, 11:35
vksunder wrote:
Which of the following is equal to (2^k)(5^k − 1)?



A. 2(10^k − 1)
B. 5(10^k − 1)
C. 10^k
D. 2(10^k )
E. 10^2k − 1



2^k*5^{k − 1}= \(2*2^{k-1}*5^{k-1} =2*10^{k-1}\)

A
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Re: Exponents [#permalink]

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New post 01 Oct 2008, 11:41
can you please re-post the question with the () clearly posted..i cant really follow the question as posted..

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Re: Exponents [#permalink]

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New post 01 Oct 2008, 11:44
Me neither - I could not understand the question?

I tried working with plugin numbers
Let k=2

2^2(5^2 – 1) = 4( 24) = 96

A 2*99 = gone
B 5*99 = gone
C 100 = gone
D 2*100 = gone
E 10^2*2-1 = gone

Confused!!

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Re: Exponents [#permalink]

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New post 01 Oct 2008, 12:04
(2^k)(5^k − 1)?
should be \(2^k 5^{k-1}\)
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New post 01 Oct 2008, 12:15
plug in should work too

replace k with 2

u should get 2^2*5^(2-1) = 4*5=20

choice A also produces 20 when k is replaced w 2

2*(10)=20
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Re: Exponents [#permalink]

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New post 01 Oct 2008, 12:49
x2suresh wrote:
(2^k)(5^k − 1)?
should be \(2^k 5^{k-1}\)



Yep there is a lot of different between \(2^k 5^{k-1}\) & \(2^k {5^k -1}\)

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New post 01 Oct 2008, 13:32
Suresh - thanks for correcting the error and also for the explanation.

Sorry for the confusion guys!

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Re: Exponents [#permalink]

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New post 01 Oct 2008, 14:20
lol me too the did make the mistake but when I rechecked it by plugging numbers it was clear.

question can be written as

2*{2^(k-1)*5^(k-1)}
2*{10^(k-1)} ........ans A

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Re: Exponents [#permalink]

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New post 01 Oct 2008, 18:09
Guys, shldnt the answer choice A be 2(10^(k-1))?
There is a difference b/w 2(10^(k-1)) and 2(10^k − 1)
vksunder wrote:
Which of the following is equal to (2^k) [5^(k − 1)]?



A. 2(10^k − 1)
B. 5(10^k − 1)
C. 10^k
D. 2(10^k )
E. 10^2k − 1

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Re: Exponents [#permalink]

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New post 01 Oct 2008, 22:42
vksunder wrote:
Which of the following is equal to (2^k) [5^(k − 1)]?



A. 2(10^k − 1)
B. 5(10^k − 1)
C. 10^k
D. 2(10^k )
E. 10^2k − 1


IMO A
10^k /5 => 10 * 10^k /5 => 2* 10^(k-1) => A is answer
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Re: Exponents   [#permalink] 01 Oct 2008, 22:42
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Which of the following is equal to (2^k) ? A. 2(10^k 1) B.

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