Why is this equation true? (rules of exponents, I assume)

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

It has been a while since ive done algebra, but I cant figure out why this is all equal. Can someone help me out here?

I assume its related to rules of exponents but when I look online its mostly simpler stuff that I cant see relating to this (such as x*x=x^2 etc)

Re: Why is this equation true? (rules of exponents, I assume)

Quote:

Originally Posted by

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

It has been a while since ive done algebra, but I cant figure out why this is all equal. Can someone help me out here?

I assume its related to rules of exponents but when I look online its mostly simpler stuff that I cant see relating to this (such as x*x=x^2 etc)

Surely you know that $\displaystyle 1+\frac{n-2}{2}=\frac{n}{2}~?$

Re: Why is this equation true? (rules of exponents, I assume)

Quote:

Originally Posted by

**Plato** Surely you know that $\displaystyle 1+\frac{n-2}{2}=\frac{n}{2}~?$

I can tell that it is by substituting values for n, but I dont know anything else. Is this something that people tend to have memorized? If so, I may have forgotten, as I have a bad memory.

Re: Why is this equation true? (rules of exponents, I assume)

common denominator

$\displaystyle \frac{2}{2} + \frac{n-2}{2} = \frac{2 + (n-2)}{2} = $ ...