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Would doing this be considered wrong even if I get the right answer?

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rewrite the exspression as (4\^x)-(4\^x)(4\^-1). Then factor out the 4\^x and simplify
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Depends on context. On a timed multiple choice, or even free (short) response, test where it isn’t necessary to show work, that would be a valid test-taking strategy.
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We have : 4^x - 4^x-1= 4^x - 4^x /4 : ©
We make a variable change for the sake of clarity and also to see the pattern.
T=4^x ; From © We now have:
T - T/4 = 4×T/4 -T/4    (Multiplied and divided by the same number)
Now that we have the same denominator we can Compose the terms.
4×T/4 - T/4 = (4T-T)/4
                      = 3T/4
                      =3/4×T
We now have:
T _ T/4 = 3/4 T Wich is the same as:
4^x - 4^x-1 = 3/4 × 4^x.
I Hope this is helpful.
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Actually, this is a perfectly fine way to start problem.  If the expression is true for all x, then it's true for x=0.  This is a great way to get a feel for how things work.

Now, though, you still have to show the result you got works for other values of x

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