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# How does 1000^12 = 10^36 and 2^24 = 2^4 * 10^6

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Manager
Joined: 07 Jul 2013
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How does 1000^12 = 10^36 and 2^24 = 2^4 * 10^6 [#permalink]

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16 Jul 2013, 20:35
How does 1000^12 = 10^36 and 2^24 = 2^4 and 10^6, i've been trying to understand this for the last hour, I have the kaplan premier and it does not really go into detail on exponents.
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Re: How does 1000^12 = 10^36 and 2^24 = 2^4 * 10^6 [#permalink]

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16 Jul 2013, 20:43
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laserglare wrote:
How does 1000^12 = 10^36 and 2^24 = 2^4 and 10^6, i've been trying to understand this for the last hour, I have the kaplan premier and it does not really go into detail on exponents.

Actually, 1000 =10^3
Therefore, 1000^12 =(10^3)^12=10^36

However 2^24 can not be 2^4 and 10^6. Please check from where you copied it.

My advice, you may want to follow Bunuel. His signature has lots of problems, corresponding solutions and the theory as well.
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Re: How does 1000^12 = 10^36 and 2^24 = 2^4 * 10^6 [#permalink]

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16 Jul 2013, 20:56
also why does 1^-1...lol i clearly need to review exponents

it was from #5 of the gmat club diagnostic, i found out they used an approximation.....2^10 = 10^3

so therefore 2^24 = 2^4 * 2^20 = 2^4 * 10^6

anyways thanks for the explanation, it helps tremendously...
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Re: How does 1000^12 = 10^36 and 2^24 = 2^4 * 10^6 [#permalink]

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16 Jul 2013, 22:53
Expert's post
laserglare wrote:
also why does 1^-1...lol i clearly need to review exponents

it was from #5 of the gmat club diagnostic, i found out they used an approximation.....2^10 = 10^3

so therefore 2^24 = 2^4 * 2^20 = 2^4 * 10^6

anyways thanks for the explanation, it helps tremendously...

$$2^{24} =2^4*2^{20}=2^4*(2^{10})^2$$. Now, since $$2^{10}=1024\approx 10^3$$ then $$2^4*(2^{10})^3\approx{2^2*(10^3)^2}=2^4 * 10^6$$.

The question you are talking abut is dicsussed here: gmat-diagnostic-test-question-79333.html#p765859

Theory on Exponents: math-number-theory-88376.html

DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

Hope it helps.
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Re: How does 1000^12 = 10^36 and 2^24 = 2^4 * 10^6   [#permalink] 16 Jul 2013, 22:53
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# How does 1000^12 = 10^36 and 2^24 = 2^4 * 10^6

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