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# 3^(-n)*3^(-n) = 1/81, what is the value of n?

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Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 18

Kudos [?]: 50 [0], given: 220

3^(-n)*3^(-n) = 1/81, what is the value of n? [#permalink]  12 Nov 2017, 00:02
00:00

Question Stats:

66% (00:47) correct 33% (01:37) wrong based on 3 sessions
$$3^{-n}*3^{-n} = \frac{1}{81}$$, what is the value of n?

(A) -2

(B) 0

(C) 1

(D) 2

(E) 4

Kudos for correct solution.
[Reveal] Spoiler: OA
Director
Joined: 03 Sep 2017
Posts: 520
Followers: 1

Kudos [?]: 360 [1] , given: 66

Re: 3^(-n)*3^(-n) = 1/81, what is the value of n? [#permalink]  12 Nov 2017, 23:26
1
KUDOS
We know that $$3^{-n}3^{-n} = 3^{-2n}$$, then we can rewrite $$3^{-2n} = \frac{1}{3^{2n}}$$ to facilitate the comparison with 1/81.

Now we have to check which value of n makes $$3^{2n} = 81$$. Since 81 = 2^4, 2n = 4, thus n = 2.

Re: 3^(-n)*3^(-n) = 1/81, what is the value of n?   [#permalink] 12 Nov 2017, 23:26
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