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If n=10^{100} and n^{n}=10^{k}, what is the value of k?

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If n=10^{100} and n^{n}=10^{k}, what is the value of k?  [#permalink]

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New post 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?  [#permalink]

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New post 19 Apr 2015, 10:16
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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?  [#permalink]

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New post 20 Apr 2015, 03:20
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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.\(100^{10}^{100}\)

Could someone explain me the reasoning behind the answer please? thanks!


Similar question to practice: if-n-10-10-and-n-n-10-d-what-is-the-value-of-d-159713.html
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Re: If n=10^{100} and n^{n}=10^{k}, what is the value of k?  [#permalink]

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New post 22 May 2016, 07:55
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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?  [#permalink]

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New post 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?  [#permalink]

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New post 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?  [#permalink]

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