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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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  • $\begingroup$ What does this have to do with normal distributions? $\endgroup$ Feb 28 '12 at 4:19
  • $\begingroup$ @DilipSarwate I retagged OP's question. $\endgroup$
    – user2468
    Feb 28 '12 at 4:28
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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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  • $\begingroup$ Yes, but do you have to break it down any farther? If it needs to be a single number? $\endgroup$
    – SNS
    Feb 28 '12 at 4:21
  • $\begingroup$ First let's make we using the same definition en.wikipedia.org/wiki/Scientific_notation $\endgroup$
    – user2468
    Feb 28 '12 at 4:22
  • $\begingroup$ 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 $5000$. $\endgroup$
    – user2468
    Feb 28 '12 at 4:24
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    $\begingroup$ Nooo! $ 4\times 10^{5000} \color{red}{\neq} 40^{5000}$. Simpler example: $4 \times 10^2 = 400,$ whereas $40^2 = 1600$. $\endgroup$
    – user2468
    Feb 28 '12 at 4:26
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    $\begingroup$ That example 1.7x10^5 would fit better since it is a better approximation! $\endgroup$
    – checkmath
    Feb 28 '12 at 4:54

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