desiguy wrote:

x=10^100, x^x=10^k

k=?

10^5

10^102

10^99

10^200

10^98

Please show your calcs...

That one is easy.

Fill in the first equation with the content of the second. You get:

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

The crux is the following. On both sides of the equation you have 10 as the base, you must now find out k. Simplify:

(10^10^2) ^ (10^100) = 10^k

Now you can multiply the exponents.

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

Focus on the equation inside the parentheses. Since you have the same base you can add 2 and 100. The result is

10^102