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What is the value of N such that (-2)^(2N) = 16^2

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Bunuel
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What is the value of N such that (-2)^(2N) = 16^2 [#permalink] New post  06 Feb 2020, 05:52
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What is the value of N such that \((-2)^{(2N)}=]16^2\)

A. -4
B. 2
C. 4
D. 8
E. 16
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BrentGMATPrepNow
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Re: What is the value of N such that (-2)^(2N) = 16^2 [#permalink] New post  06 Feb 2020, 07:43
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Bunuel wrote:
What is the value of N such that \((-2)^{(2N)}=16^2\)

A. -4
B. 2
C. 4
D. 8
E. 16


Alternatively, if we recognize that \((-2)^4 = 16\), we can rewrite the original equation using a base of \(-2 \)

Take: \((-2)^{(2N)}=16^2\)

Rewrite the right side as follows: \((-2)^{(2N)}=[(-2)^4]^2\)

Simplify the right side: \((-2)^{(2N)}=(-2)^8\)

Now that both sides have the same base we can conclude that: \(2N = 8\), which means \(N = 4\)

Answer: C

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Re: What is the value of N such that (-2)^(2N) = 16^2 [#permalink] New post  06 Feb 2020, 06:42
What is the value of N such that \((−2)^(2N)= 16^2\)

A. -4
B. 2
C. 4
D. 8
E. 16

(-2)^2N can be written as \((-2^2)^N -> 4^N = 4^4 -> N=4\) -> Answer - C
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Re: What is the value of N such that (-2)^(2N) = 16^2 [#permalink] New post  06 Feb 2020, 07:24
Bunuel wrote:
What is the value of N such that \((-2)^{(2N)}=]16^2\)

A. -4
B. 2
C. 4
D. 8
E. 16


\((-2)^{(2N)}=16^2\)

\((16)^2==>(4^2)^2 ==> (4)^4 ==> (2^2)^4 ==> (-2)^{2*4} \)

Hence C
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Abhishek009
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Re: What is the value of N such that (-2)^(2N) = 16^2 [#permalink] New post  06 Feb 2020, 07:26
Bunuel wrote:
What is the value of N such that \((-2)^{(2N)}=]16^2\)

A. -4
B. 2
C. 4
D. 8
E. 16


\(16 = 2^4\)

Now, \((-2)^{(2N)}= 2^8\)

\(-2^{2n}\) = Always have +ve value as the power is even...

So, \(2N = 8\)

Or, \(N =4\), Answer must be (C)
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Re: What is the value of N such that (-2)^(2N) = 16^2 [#permalink] New post  21 Feb 2021, 11:47
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Re: What is the value of N such that (-2)^(2N) = 16^2 [#permalink]
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