Misc. questions on powers and surds.

and everyone knows I fit that bill...

1. If \frac{1}{2}^ - 3 = 2^3 ; why does 2^-17 not equal 1/2 ^17?

2. if \sqrt{7} + \sqrt{7} can be denoted as \sqrt{7 + 7} ; why can't the (\sqrt{7} + \sqrt{7})^2 be denoted as (\sqrt{7 + 7})^2 = 14?

3. if m^ -1 = - \frac{1}{3}. would m^ 1 = - 3, AND would m^ -2 = 1/9?

4. if we have a simplified function \frac{\sqrt(n+1) + \sqrt{n}}{n+1 - n} , how does the denominator divided into the numerator give us the numerator?

5. You have a term (10^4 - 10^2)(0.0012 repeated). My initial instincts would be (10^4 - 10^2) = (10^2) and multiply that by (0.0012 repeated). I would assume I'm wrong?

6. Why isn't latex working :)?

I'll grasp this if it kills me!