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# If 3^(2n) = (1/9)^(n+2), what is the value of n?

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Joined: 02 Sep 2009
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If 3^(2n) = (1/9)^(n+2), what is the value of n?  [#permalink]

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21 Mar 2016, 07:38
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If $$3^{(2n)} = (\frac{1}{9})^{(n+2)}$$, what is the value of n?

A. -2
B. -1
C. 0
D. 1
E. 2

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Re: If 3^(2n) = (1/9)^(n+2), what is the value of n?  [#permalink]

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22 Mar 2016, 00:51
1
3^(2n) = 3^(-2n - 4)
Equate the powers: 2n = -2n - 4
4n = -4
n = -1

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Joined: 12 Sep 2015
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If 3^(2n) = (1/9)^(n+2), what is the value of n?  [#permalink]

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22 Mar 2016, 15:10
1
Bunuel wrote:
If $$3^{(2n)} = (\frac{1}{9})^{(n+2)}$$, what is the value of n?

A. -2
B. -1
C. 0
D. 1
E. 2

For these kinds of questions, we typically must rewrite the terms so that they have the SAME BASES.
One option is to rewrite the right hand side with a power of 3.

Given: 3^(2n) = (1/9)^(n + 2)
Rewrite 1/9 to get: 3^(2n) = [3^(-2)]^(n + 2)
Apply Power of a Power law to get: 3^(2n) = 3^(-2n - 4)
We can now conclude that 2n = -2n - 4
Solve, to get: n = -1

RELATED RESOURCES:
- Laws of exponents – part I: https://www.gmatprepnow.com/module/gmat ... video/1025
- Negative exponents: https://www.gmatprepnow.com/module/gmat ... video/1028
- Laws of exponents – part II: https://www.gmatprepnow.com/module/gmat ... video/1029
- Solving equations with exponents: https://www.gmatprepnow.com/module/gmat ... video/1043

Cheers,
Brent
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Re: If 3^(2n) = (1/9)^(n+2), what is the value of n?  [#permalink]

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22 Mar 2016, 15:15
1
1/9 is the reciprocal of 3 so the exponent of 3 should negative -> answer choices C, D, and E are eliminated.

By replacements:
Left-hand side: 3^-2 = 1/3^2 = 1/9
Right-hand side: (1/9)^2+(-1) = (1/9)^1 = 1/9

The correct answer choice is B
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If 3^(2n) = (1/9)^(n+2), what is the value of n?  [#permalink]

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31 Jul 2017, 06:41
Bunuel wrote:
If $$3^{(2n)} = (\frac{1}{9})^{(n+2)}$$, what is the value of n?

A. -2
B. -1
C. 0
D. 1
E. 2

1/9= 3^-2

So, 3^(2n) = 3^(-2n - 4)
Equating the powers: 2n = -2n - 4
4n = -4
n = -1

B is the answer
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If 3^(2n) = (1/9)^(n+2), what is the value of n?   [#permalink] 31 Jul 2017, 06:41
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# If 3^(2n) = (1/9)^(n+2), what is the value of n?

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