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I chose A and it was obviously incorrect but I can't figure out why. I thought that I could multiply exponents, doesn't that mean that I would essentially have, -(10^10)^(10^10) = 10^d -10^10.10.10 = 10^d -10^1000 = 10^d d= 1,000 = 10^3?

Re: If n = 10^10 and n^n = 10d, what is the value of d? [#permalink]

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13 Sep 2013, 19:47

russ9 wrote:

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

10^3 10^10 10^11 10^20 10^100

I chose A and it was obviously incorrect but I can't figure out why. I thought that I could multiply exponents, doesn't that mean that I would essentially have, -(10^10)^(10^10) = 10^d -10^10.10.10 = 10^d -10^1000 = 10^d d= 1,000 = 10^3?

Why doesn't that work?

Thanks!

Hi,

n^n= =(10^10)^(10^10) this can be written as = 10^(10*10^10) =10^(10^11)

but I still have a problem in applying it to this question

Yes, I guess many people will have a similar feeling. Think of it not in terms of exponents but simple numbers.

Imagine what 10^10 is: n = 10000000000 (it has 10 zeroes) \(n^n = 10000000000^{10000000000} = (10^{10})^{10000000000} = 10^{100000000000}\) (now it has 11 zeroes) \(10^d = 10^{100000000000}\)

So \(d = 100000000000 = 10^{11}\)
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Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]

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30 Jun 2015, 08:32

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Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]

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