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What is the value of N such that (-2)^(2N) = 16^2
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21 Feb 2021, 10:47
21 Feb 2021, 10:47
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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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. -4
B. 2
C. 4
D. 8
E. 16
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Re: What is the value of N such that (-2)^(2N) = 16^2
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21 Feb 2021, 10:58
21 Feb 2021, 10:58
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Solution:
We can start by converting 16=\(2^4\)
\((-2)^2^N=2^4^*^2\)
=\(2^8\)
As \(2^8=-2^8\) because and even power always yields a positive value
2N=8
N=4
IMO C
Hope this helps!
We can start by converting 16=\(2^4\)
\((-2)^2^N=2^4^*^2\)
=\(2^8\)
As \(2^8=-2^8\) because and even power always yields a positive value
2N=8
N=4
IMO C
Hope this helps!
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Joined: 10 Apr 2015
Posts: 6218
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Re: What is the value of N such that (-2)^(2N) = 16^2
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21 Feb 2021, 12:08
21 Feb 2021, 12:08
Carcass wrote:
What is the value of N such that \((-2)^{(2N)}=16^2\)
A. -4
B. 2
C. 4
D. 8
E. 16
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. -4
B. 2
C. 4
D. 8
E. 16
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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
Cheers,
Brent
