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If 5^2^1 X 4^1^1 = 2 X 10^n what is the value of n?

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If 5^2^1 X 4^1^1 = 2 X 10^n what is the value of n? [#permalink]  09 Jan 2009, 08:40
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If $$5^2^1 X 4^1^1 = 2 X 10^n$$ what is the value of n?

o 11
o 21
o 22
o 23
o 32

Hi, has someone a quick way of getting this done?

Answer A is correct (not E as indicated).

many Thx
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Re: GMAT Prep - Exponent Problem [#permalink]  09 Jan 2009, 08:48
I may be wrong; now I get B.

5^21x4^11 = 5^21x2^21x2=2x(5x2)^21
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tusharvk

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Re: GMAT Prep - Exponent Problem [#permalink]  09 Jan 2009, 08:57
sorry it is B
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Re: GMAT Prep - Exponent Problem [#permalink]  09 Jan 2009, 09:06
thanks so far....but can you expalain your step from
4^11 to 2^21x2 ?

many thanks
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Re: GMAT Prep - Exponent Problem [#permalink]  09 Jan 2009, 10:24
Oh I apologize; in my excitement I just jumped off.
5^21x4^11 = 5^21x(2^2)^11 = 5^21x2^22 = 2x2^21x5^21=2x(5x2)^21=2x10^21.

best.
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tusharvk

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Re: GMAT Prep - Exponent Problem [#permalink]  09 Jan 2009, 12:46
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tusharvk wrote:
Oh I apologize; in my excitement I just jumped off.
5^21x4^11 = 5^21x(2^2)^11 = 5^21x2^22 = 2x2^21x5^21=2x(5x2)^21=2x10^21.

best.

2 = 2^1
10^N = 2^N X 5^N

2 X 10^N = 2^(N+1) X 5^N

4^11 = 2^11 X 2^11
SO:
5^21 X 2^22 = 2^(N+1) X 5^N

Drop the bases and the answer is clearly 21.
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Re: GMAT Prep - Exponent Problem [#permalink]  15 Jan 2009, 03:49
Re: GMAT Prep - Exponent Problem   [#permalink] 15 Jan 2009, 03:49
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