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Adding exponents

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Joined: 08 Jul 2009
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Adding exponents [#permalink]

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New post 30 Jul 2009, 18:56
I'm sure this question has been asked, but it's hard to search for:

2^1 +2^1 +2^2+ 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 =

I'm having trouble factoring it out.

Thank you!

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Re: Adding exponents [#permalink]

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New post 30 Jul 2009, 19:28
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2^1 +2^1 +2^2+ 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8

2^1 +2^1 = 2*2^1 = 2^2
2^2 + 2^2 = 2*2^2 = 2^3

So 2^1 +2^1 +2^2 form 2^3
Similarly 2^1 +2^1 +2^2+ 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 is equal to 2^9

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Re: Adding exponents [#permalink]

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New post 31 Jul 2009, 12:43
[EDIT - REMOVED BY USER]

Last edited by nplaneta on 17 Jun 2012, 17:39, edited 1 time in total.

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Re: Adding exponents [#permalink]

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New post 31 Jul 2009, 16:47
Excellent, thank you!

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Re: Adding exponents [#permalink]

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New post 01 Jan 2011, 23:00
nplaneta wrote:
Aleehsgonji wrote:
2^1 +2^1 +2^2+ 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8

2^1 +2^1 = 2*2^1 = 2^2
2^2 + 2^2 = 2*2^2 = 2^3

So 2^1 +2^1 +2^2 form 2^3
Similarly 2^1 +2^1 +2^2+ 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 is equal to 2^9



I was stumped by this as well. Great explaination. Kudos to you.


Very Nice Explanation..
U have made it so very precise and clear..

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Re: Adding exponents [#permalink]

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New post 22 Oct 2011, 02:24
Thanks a lot. It. Looks so easy now!

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Re: Adding exponents [#permalink]

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New post 27 Oct 2011, 21:37
Alternate solution (not really practical here but maybe in a similar problem?):

2^1 +2^1 +2^2+ 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ?

Represented in binary:

0000000010 +
0000000010 +
0000000100 +
0000001000 +
0000010000 +
0000100000 +
0001000000 +
0010000000 +
0100000000 =
----------------
1000000000

I've just started my GMAT prep recently so feel free to disregard if this doesn't sound helpful, but changing bases can be helpful sometimes =]

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Re: Adding exponents   [#permalink] 27 Oct 2011, 21:37
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