If N = 10^10

imago · Posted: Sun Sep 16, 2007 12:29 pm Post subject: If N = 10^10

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

niks_01.27 · Posted: Sun Sep 16, 2007 1:10 pm Post subject:

Substitute the value of both N's in;

N^N = 10^k.

You will get k = 10^102.

optimisticsam · Posted: Sun Sep 16, 2007 1:23 pm Post subject:

Little fuzzy on this one still - anyone care to explain a little further?

kajcha · Posted: Sun Sep 16, 2007 1:49 pm Post subject:

(x^y)^z can be written as (x)^(y*z).

In this case N = 10^100

N^N = (10^100)^(10^100) = 10^k

= 10^(100*(10^100)) = 10^k

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

imago · Posted: Sun Sep 16, 2007 3:33 pm Post subject:

optimisticsam · Posted: Sun Sep 16, 2007 3:58 pm Post subject:

Ah! Got it. Thanks!

I was forgetting that (x^a)(x^b) = x^(a+b)

Thanks for clarifying! Very helpful!