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amastu
(−8)^(2n)=2^(8+2n)
(-2)^6n= 2^(8+2n)
If positive, negative does not matter
6n = 8+2n
n=4
D

Hi

When you wrote 6n=8+2n, you will get
6n-2n = 8 or 4n = 8 or n=2.

Your approach is correct, probably there was a typo so I am pointing that out.
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Bunuel
If n is a number such that \((−8)^{(2n)} = 2^{(8+2n)}\), then n =

(A) 1/2
(B) 3/2
(C) 2
(D) 4
(E) 5

\((−8)^{(2n)} = 2^{(8+2n)}\)

Or, \((−2)^{(3*2n)} = 2^{(8+2n)}\)

Or, \({(6n)} = {(8+2n)}\)

Or, \(6n = 8 + 2n\)

Or, \(4n = 8\)

Or, \(n = 2\)

So, Answer must be (C) 2
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Bunuel
If n is a number such that \((−8)^{(2n)} = 2^{(8+2n)}\), then n =

(A) 1/2
(B) 3/2
(C) 2
(D) 4
(E) 5

The negative sign in front of the 8 will be eliminated because we are raising a negative number (-8) to an even power. Note that (-8)^(2n) = [(-8)^2]^n = [8^2]^n = 8^(2n). Then:

8^(2n) = (2^3)^(2n) = 2^(6n) = 2^(8 + 2n)

Since bases are the same, we can equate the exponents:

6n = 8 + 2n

4n = 8

n = 2

Answer: C
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Answer is C:
I guess the only thing which is confusing for student here is
(−8)^(2n)=2^(8+2n)
On left there is negative sign but keep in mind since n will need to be multiplied with even number so result is always even which in turn make bracket value positive
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(−8)^(2n) will always result into positive number. Hence correct option is C.
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