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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?
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13 Sep 2013, 20:47

1

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)

Re: If n = 10^10 and n^n = 10^d, what is the value of d?
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24 Feb 2014, 22:40

9

2

SaraLotfy wrote:

I know we should apply this rule:

\((a^m)^n\)=\(a^{mn}\)

a\(^m^n\)=\(a^{(m^n)}\)and not \((a^m)^n\)

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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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!

Given => \(n = 10^{10}\) -----(1) => \(n^n = 10^d\)------(2)

Now from (2) we have => \(n^n = 10^d\) => OR \(n = 10^{\frac{d}{n}}\) => OR \(10^{10} = 10^{\frac{d}{n}}\)---- substituting 'n' from (1) in LHS

Since base is same comparing both the sides we have => \(10=\frac{d}{n}\)

=> OR \(d=10*n\) => OR \(d=10*10^{10}\) ------ substituting 'n' from (1)

Re: If n = 10^10 and n^n = 10^d, what is the value of d?
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26 Aug 2018, 05:58

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Top Contributor

russ9 wrote:

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

A. 10^3 B. 10^10 C. 10^11 D. 10^20 E. 10^100

A slightly different approach....

Given: n = 10^10

Also given: n^n = 10^d Replace n in the base with 10^10 to get: (10^10)^n = 10^d Apply Power of a Power rule on left side to get: 10^10n = 10^d So, we can conclude that 10n = d Now replace the remaining n with 10^10 to get: 10(10^10) = d This is the same as: (10^1)(10^10) = d Apply Product rule to get: 10^11 = d