Alan

For each music player divide the number of dollars by the number of gigabytes and see which result is smaller. 

Neither.  If x² = -1 then x = ±i , where i is the square root of minus 1.

$$\frac{(u^3\times u^6)^4}{8u^2}=\frac{(u^9)^4}{8u^2}=\frac{u^{36}}{8u^2}=\frac{u^{34}}{8}$$

Yes.  Type in factor(N), where N is your number and press enter. e.g.

$${factor}{\left({\mathtt{50}}\right)} = {\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{2}}}$$ 

125^2/3 = 5² = 25

25^1/2 = 5

So: 125^2/3/25^1/2 = 25/5 = 5

(2x - 3)*(x + 5) = 2x² +7x -15

You're right Melody!  The absence of brackets causes a lot of confusion!

Use the fact that (x^a)^b = x^a*b

(2^5/2)³ = 2^15/2 = 2⁷*2^1/2 = 128√2

Let r be the number.

r*5/2 + 2/3 = -7/12

r*5/2 + 8/12 = -7/12

r*5/2 = -7/12 -8/12

r*5/2 = -15/12

r = -(15/12)*(2/5)

r = -3/6 = -1/2