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Intern
Joined: 30 Mar 2015
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If n=10^{100} and n^{n}=10^{k}, what is the value of k?
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19 Apr 2015, 09:42
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If n=\(10^{100}\) and \(n^{n}\)=\(10^{k}\), what is the value of k? A. 200 B. \(10^{100}\) C. \(10^{102}\) D. \(100^{100}\) E.\(100^{10}^{100}\) Could someone explain me the reasoning behind the answer please? thanks!
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Re: If n=10^{100} and n^{n}=10^{k}, what is the value of k?
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19 Apr 2015, 10:16
Hi Petu
There is a simple logic to this question. (a^m)^n = a^mn So, (10^100)^(10^100) = 10^(100*(10^100)) = 10^((10^2)*(10^100)) = 10^(10^102) and this equals 10^k So, k = 10^102 Hope this is clear




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Re: If n=10^{100} and n^{n}=10^{k}, what is the value of k?
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20 Apr 2015, 03:20



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Re: If n=10^{100} and n^{n}=10^{k}, what is the value of k?
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22 May 2016, 07:55
We know that: n=10^100 n^n=10^K
So, if you replace the first "n" (the green), you have : 10^100n = 10^k
So, 100 n = k (10^2) n = K
So, 10^100+2 = K



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Re: If n=10^{100} and n^{n}=10^{k}, what is the value of k?
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22 May 2016, 07:57
petu wrote: If n=\(10^{100}\) and \(n^{n}\)=\(10^{k}\), what is the value of k?
A. 200
B. \(10^{100}\)
C. \(10^{102}\)
D. \(100^{100}\)
E.\(100^{10}^{100}\)
(10^100)^10^100= 10^10^2*10^100= 10^102 C is the answer
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Re: If n=10^{100} and n^{n}=10^{k}, what is the value of k?
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27 Oct 2016, 17:57
Trick for this one is to rewrite 100 as 10^2 >A lightbulb will go off if you've reviewed roots.
10^100=10^(10^2)
so...10^[(10^2)^(10^100)] = 10^[10^102] = 10^K > K = 10^102



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Re: If n=10^{100} and n^{n}=10^{k}, what is the value of k?
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07 Sep 2018, 11:05
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