How can I centralize vertically roots in an equation?

Question

When I execute this code

\documentclass[11pt]{article}
\begin{document}    
$\sqrt[n]{a\cdot b}=\sqrt[n]{a}\cdot \sqrt[n]{b}$
\end{document}

the individual equations on the right side are not centralized.

Is there a way to align them vertically?

Thank you! Igor

Answer 1

One option is to add a \vphantom for the larger argument in the smaller one:

$\sqrt[n]{a\cdot b}=\sqrt[n]{\vphantom{b}a}\cdot \sqrt[n]{b}$