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If I were trying to change a problem with exponents into a scientific notation how would I do that?

Example is $4(10^{50})^{100}$

I will have questions like this on an exam and I need to understand how to do it. Thank you.

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    What does this have to do with normal distributions?2012-02-28
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    @DilipSarwate I retagged OP's question.2012-02-28

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Since $$(10^{50})^{100} = 10^{50 \times 100} = 10^{5000}$$ we have $$4(10^{50})^{100} = 4 \times 10^{5000}$$

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    Yes, but do you have to break it down any farther? If it needs to be a single number?2012-02-28
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    First let's make we using the same definition http://en.wikipedia.org/wiki/Scientific_notation2012-02-28
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    I'd multiply out everything and then divide the result by the largest power of $10$ such that the quotient is a single digit. Example: $$ 4(10^{50})^{100} = 4(10^{5000}) $$ Now, the largest such power of $10$ is $5000$.2012-02-28
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    Yes, that is what I am talking about. I guess what I mean is would you multiply the 4 and the 10 making it 40^5000?2012-02-28
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    Nooo! $ 4\times 10^{5000} \color{red}{\neq} 40^{5000}$. Simpler example: $4 \times 10^2 = 400,$ whereas $40^2 = 1600$.2012-02-28
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    That makes sense but if it needs to be a single number in scientific form I am still confused.2012-02-28
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    Hm, I will another way: multiply out the result as if you are carrying out normal arithmetic. So for example: $423 \times 20^2 = 169200.$ Now, to convert that into single digit, keep dividing out by $10$ until you are left with a single. During the process record the number of $10$'s. For $169200$, you will need to divide out by $10$ $\color{red}{\mbox{five}}$ times, i.e., $169200$ is approximately $1.6 \times 10^5$.2012-02-28
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    You can always click the checkmark to the left to accept my answer when you are satisfied with the answer. I shamelessly enjoy my reputation points :)2012-02-28
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    That example 1.7x10^5 would fit better since it is a better approximation!2012-02-28