there is this one step that is throwing me off.. in math can you help me?

Question

2^1*2^(n-1)
Then
2^(n-1+1)
2n... many of you would understand this but what i don;t understand is where did multiply 2 go... it wasnt divided by 2 so its not neutralized ?? but somehow its not there and this must make sence.. to me it doesn't please explain..

Answer 1

(2^1)(2^(n-1))
if they have the same base number (in this case, 2) you add the exponents of the number. and then there will be only one term with the base number.

Answer 2

My pleasure.
2^3*2^4 means 2 X 2 X 2 X 2 X 2 X 2 X 2= 128
Now 2^7=128. I see I could have simply added the exponents to get 2^3*2^4=2^(3+4)=2^7

It turns out to be always true, and so we can make a math rule: a^r X a^s=a^(r+s). This holds true only if the base is identical.
In your problem, you have identical bases,(2), so you can use this rule.
Your math was correct: 2^1*2^(n-1)= 2^(n-1+1)=2^n
I hope this answers your question

Answer 3

it's a rule with exponents, when you multiply like bases with different exponents (like that you are doing) you can combine them into one expression of the like base (in your case 2) and raise it to the sum of the powers (for you 1+ (n-1))

for division you end up subtracting the powers.

Answer 4

When you multply, exponents are added.

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