simplifying with exponents that must be positive

Question

$$\frac{\sqrt{c\cdot \:a^2}\cdot \:b^2}{c^2\cdot \left(a^{-1}\cdot \:b^3\right)^{-3}}$$

Now this should simplify to

$$\frac{b^{11}\sqrt{c}}{c^2a^2}$$

My question is why is it important that $a, b$ and c$ variables are positive ?

Answer 1

If the numbers were negative, then $\sqrt{c\cdot a^2}$ would have a negative number inside the radical. Obviously this can't be true for real numbers, so all numbers must be positive.

In general, when $n$ is even, $\sqrt[n]{a^n} = |a|.$