Math question for anyone in grade 11 or higher?

Question

I'm not in grade 11..but my friend is and i'm trying to help him so if you could help me, that would be awesome.. =)

2^-n(2^n-2^1+n)

Answer 1

The answer is simply -1

= 2^(-n) is the same as 1 / 2^n

So this can be rewritten as:
= [ 2^n - 2^(1+n) ] / 2^n

You can distribute the 2^n so it is now:
= 2^n / 2^n - 2^(1+n) / 2^n

Simplifying further:
= 1 - 2^(1+n) / 2^n

When you divide two powers (2^(1+n) / 2^n), it is the same as subtracting the exponents:

= 1 - 2^(1+n-n)
= 1 - 2^1
= 1 - 2
= -1

You can test this by picking a value for n, let's say 4.
2^-4(2^4 - 2^5)
= 1/16 * (16 - 32)
= 1/16 * (-16)
= -1

So however you look at it, the answer is -1.

Answer 2

It's a little unclear what the exponents are. I'm interpreting this as

2^(-n)*(2^n-2^(1+n))

Using the distributive property, this would be

2^(-n+n)-2^(-n+1+n)

2^0-2^1

1 - 2 = -1

Of course, the answer could be something different if I've misinterpreted the original problem. Your rendition was a bit ambiguous.

Answer 3

Alright, the n is negative so its 2/n * x.
x = 2^n + n -2.
Distributive prop. says:
(2/n * 2^n) + (2/n * n) + (2/n * -2) =

4^n/n + 2 + -4/n =

4^n/n -4/n +2

Im not sure but it could be something else. when I did the problem the first time, I got -1, but now its different. I did it again and I got the above.

Answer 4

This is the same as:

(2^n - 2 + n)
---------------
2^n

= 1 - 2/2^n + n/2^n

= 1 - 2^(-n + 1) + n*2^n

Answer 5

2^-n

Answer 6

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Answer 7

so i think it would be
2^2n.....wtf there's a negative sign infront of n?, ok i give up

Answer 8

4n^2 - 3n

Answer 9

2n

Answer 10

beats me