Hey, can someone please help. So not sure if helpful but I tried a few ways

First algebraically

2^-m + 2^-m = 2^-x [same base so drop the powers]

-m + -m = -x

-m - m = -x

m + m = x

2m = x

m = x/2 and chose D

then i tried choosing numbers

1/2^2 + 1/2^2 = 1/2^X

1/4 + 1/4 = 1/2^1

so x = m -1 because 2-1 = 1 then B (which is the right answer)

then i tried again with the negative powers

2^-2 + 2^-2 = 2^-1

so then m-1 doesn’t work, right? cause it would be -2 + 1 = -1

Either way, I was just trying out a couple of things and don’t get why my other options don’t give the same results. Thanks!

Gone wrong right at the start. You can’t just “drop the powers” when adding exponents. What you **can** do is something like this:

2^{-m} + 2^{-m}

= 2 \times 2^{-m} (adding the same term twice)

= 2^{1 - m} (using exponent rules)

At that point, since there is only one term at the LHS and RHS, you **can** drop the base if needed.

The problem is that you’re essentially changing the definition of *m*, when that isn’t the case. In other words, when you say that 2^{-2} + 2^{-2} = 2^{-1}, *m* is still 2, not -2. After all, from your first line, we have 2^{-m} + 2^{-m} = 2^{-x} - notice the change from *m* to -*m*. This is why we don’t change *m* itself from 2 to -2.

I think the choice is B, and this screenshot details how I would solve it.

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