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

Question

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}}

Naina1 · Accepted Answer

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

Bunuel · Answer

Similar question to practice: if-n-10-10-and-n-n-10-d-what-is-the-value-of-d-159713.html

Alex75PAris · Answer

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

Divyadisha · Answer

(10^100)^10^100= 10^10^2*10^100= 10^102

C is the answer

law258 · Answer

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^  = 10^K --> K = 10^102

bumpbot · Answer

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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?

Prep Toolkit

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