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exponent problem

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exponent problem [#permalink] New post 23 Mar 2006, 20:43
Hi could someone just show out the work for this one?

x = 10^100, x^x=10^k, k=?
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 [#permalink] New post 23 Mar 2006, 23:08
x = 10^100, x^x=10^k, k=?
substitute x with 10^100--->(10^100)^(10^100)=10^k since the base is same 10 and 10 we get k=100^(10^100)
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 [#permalink] New post 25 Mar 2006, 10:42
The answer given to this was k=102

so 10^102. For some reason I am having a hard time simplifying that
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 [#permalink] New post 25 Mar 2006, 10:53
k = 10^102

x^x = (10^100)^(10^100)

= 10^(100*(10^100))
= 10^((10^2)*(10^100))
= 10^(10^102) = 10^k
  [#permalink] 25 Mar 2006, 10:53
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