Max profit question, regarding negative exponents with factors $p= 10q^{-0,5}$
$C(q) = 5q$
In a monopoly the equation for maximum profits is: $p'(q)\cdot q + p(q) - C'(q) = 0$
First order condition:
$-0,5 \cdot 10q^{-1,5} \cdot q + 10q^{-0,5} - q = 0$ 
can't figure out onwards from here. How do I do with these negative exponents?
the answer is $q = 1$, and $p = 10$

As stated above in a comment I believe the correct equation for monopoly profit optimization should be $(-.5)\cdot 10q^{-1.5}\cdot q + 10q^{-.5} - 5 = 0$. We will solve this equation for $q$ below:
$(-.5)\cdot 10q^{-1.5}\cdot q + 10q^{-.5} - 5 = 0 \Rightarrow \frac{-5}{\sqrt{q}} + \frac{10}{\sqrt{q}} - 5 = 0$
Here we have simply used algebra of exponents: $x^{-a} = \frac{1}{x^a}$ and $(x^a)(x^b) = x^{a+b}$.
$\frac{-5}{\sqrt{q}} + \frac{10}{\sqrt{q}} - 5 = 0 \Rightarrow \frac{5}{\sqrt{q}} = 5 \Rightarrow \sqrt{q} = 1 \Rightarrow q = 1$
Thus we arrive at $q = 1$. Plugging $q$ into our equation for $p$ we see $p = 10(q)^{-.5} = 10(1)^{-.5} = 10(1) = 10$. Thus $q = 1$ and $p = 10$.
