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

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
3^(-n)*3^(-n) = 1/81, what is the value of n?  [#permalink]

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12 Nov 2017, 01:03
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Difficulty:

5% (low)

Question Stats:

92% (00:41) correct 8% (00:53) wrong based on 94 sessions

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$$3^{-n}*3^{-n} = \frac{1}{81}$$, what is the value of n?

(A) -2

(B) 0

(C) 1

(D) 2

(E) 4

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Math Expert
Joined: 02 Aug 2009
Posts: 7992
Re: 3^(-n)*3^(-n) = 1/81, what is the value of n?  [#permalink]

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12 Nov 2017, 05:19
Bunuel wrote:
$$3^{-n}*3^{-n} = \frac{1}{81}$$, what is the value of n?

(A) -2

(B) 0

(C) 1

(D) 2

(E) 4

$$x^{-y}=\frac{1}{x^y}$$...
$$3^{-n}*3^{-n}=3^{-n-n}=3^{-2n}=\frac{1}{3^{2n}}=\frac{1}{81}=\frac{1}{3^4}$$

So 2n=4.....n=2
D
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3^(-n)*3^(-n) = 1/81, what is the value of n?  [#permalink]

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12 Nov 2017, 09:57
Bunuel wrote:
$$3^{-n}*3^{-n} = \frac{1}{81}$$, what is the value of n?

(A) -2

(B) 0

(C) 1

(D) 2

(E) 4

$$3^{-n}*3^{-n} = \frac{1}{81}$$

$$3^{-n}*3^{-n} = \frac{1}{3^4}$$

$$3^{-n}*3^{-n} = 3^{-4}$$

$$-n + (-n) = -4$$
$$-2n = -4$$
$$n = 2$$

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

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18 Mar 2018, 07:06
Bunuel wrote:
$$3^{-n}*3^{-n} = \frac{1}{81}$$, what is the value of n?

(A) -2

(B) 0

(C) 1

(D) 2

(E) 4

Given $$3^{-n}*3^{-n} = \frac{1}{81}$$ ---- (1)

=> Now $$a^{-b}=\frac{1}{a^b}$$ thus $$3^{-n}= \frac{1}{3^n}$$

=> (1) becomes $$\frac{1}{3^n}*\frac{1}{3^n} = \frac{1}{81}$$
=> OR $$\frac{1}{3^{2n}}= \frac{1}{9^2}$$

=> OR $$\frac{1}{9^n}= \frac{1}{9^2}$$

=> Thus $$n=2$$

Option "D"

Thanks
Dinesh
Re: 3^(-n)*3^(-n) = 1/81, what is the value of n?   [#permalink] 18 Mar 2018, 07:06
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