lfloor and rfloor dipping down too far

Question

Why is the right-hand side delimiters going much further down than the depth of the denominator?

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\[
  \left \lfloor \dfrac{n}{p^{i+1}} \right \rfloor = 
    \left \lfloor \dfrac{\left \lfloor \dfrac{n}{p^i} \right \rfloor}{p} \right \rfloor
\]

\end{document}

Answer 1

\documentclass{standalone}
\usepackage{amsmath}

\begin{document}
$\left \lfloor \frac{n}{p^{i+1}} \right \rfloor = \left \lfloor \frac{\left \lfloor \frac{n}{p^i} \right \rfloor}{p} \right \rfloor$
\end{document}

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