If m is an integer such that (-2)^2m = 2^{9 - m}, then m=

Question

If m is an integer such that  (-2)^{2m} = 2^{9 - m} , then m=

(A) 1
(B) 2
(C) 3
(D) 4
(E) 6

Bunuel · Accepted Answer

SOLUTION

If m is an integer such that  (-2)^{2m} = 2^{9 - m} , then m=

(A) 1
(B) 2
(C) 3
(D) 4
(E) 6

First of all, since m is an integer, then 2m=even, and therefore  (-2)^{2m}=2^{2m} .

So, we'd have:

2^{2m} = 2^{9 - m} ;

2m=9-m ;

m=3 .

Answer: C.

ershovici · Answer

So, I choose C. Here is my reasoning:

-2^2m = 2^9-2
from this - (-2)^2m is the same as 2^2m, since the power is even number, so we have
2m = 9-m
3m = 9
m = 3

EMPOWERgmatRichC · Answer

Hi All,

While this question might look a little "scary", the answer choices are small numbers and we're just asked to find the one that completes the given equation, so we can use "brute force" on this question.

We're looking for the value of M that makes (-2)^(2M) = 2^(9-M)

We can work through the answers in order (although you might realize that the first couple are much TOO small, given the exponents in this prompt).

IF....
M = 1
(-2)^2 = 4
2^8 = 256
These are NOT equal

M = 2
(-2)^4 = 16
2^7 = 128
These are NOT equal

M = 3
(-2)^6 = 64
2^6 = 64
These ARE equal, so this MUST be the answer.

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

Nasahtahir · Answer

What if the question was (-2)^ 3m  = 2^9-m?
Is this possible?

Bunuel · Answer

No real m satisfies that equation.

ScottTargetTestPrep · Answer

Recall that when a negative number is raised to an even power, the result is positive. Since 2m is even, (-2)^(2m) = 2^(2m), and we have:

2^(2m) = 2^(9 - m)

2m = 9 - m

3m = 9

m = 3

Answer: C

LATIFA221B · Answer

since 2m is even, then 9-m must be even 
 we can exclude all even numbers : 2,4,6, we left with 1 and 3 
2*1 = 2 
9-1 = 8 
so one is not the solution 
2*3 = 6 
9-3 = 6 
so m = 3 .

MohammadShahriar · Answer

(-2)^2m=2^(9-m)
=> (-1*2)^2m= 2^(9-m)
=> (-1)^2m +2^2m=2^(9-m)
=>2^2m=2^(9-m)
=> 2m= 9-m
=> m=3
* whatever m is odd or even the power of -1 will always even number as multiplied by 2 and resulting in +1

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If m is an integer such that (-2)^2m = 2^{9 - m}, then m=

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If m is an integer such that (-2)^2m = 2^{9 - m}, then m=

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