What does a negative exponent in front of number mean?
Example: sin ^-1 (0.53)
This is a problem involving refraction of light through two mediums such as water and air applying Snell's Law.
In general, it means an inverse (or when dealing with numbers, a reciprocal).
In this particular example, though, $\displaystyle \sin^{-1}\!\left(0.53\right)=\arcsin\!\left(0.53\right)$. It must be emphasized that $\displaystyle \sin^{-1}\!\left(a\right)\neq\left(\sin\!\left(a\right)\r ight)^{-1}$.
Does this help??