What is the approximation for $(a x^{-2} + b x^{-4})^{-1}$ for small $x$?

Question

Given that $x$ is small (closer to zero), what should be the expression $(a x^{-2} + b x^{-4})^{-1}$ approximated with? Is it $a^{-1} x^2$ or $b^{-1} x^4$ or something else? Here, $a$ and $b$ are positive constants.

Answer 1

So you have $$(ax^{-2}+bx^{-4})^{-1} = \dfrac{x^4}{ax^2+b}\approx \dfrac{x^4}{b}\left(1-\dfrac{a}{b}x^2+O(x^4)\right)=O(x^4)$$ by Taylor's approximation.