Interesting logarithms - 1

Algebra Level 2

\begin{cases} \begin{aligned} \log_mw & = 12 \\ \log_nw & = 16 \\ \log_pw & = 36 \\ \log_{mnpq}w & = 72 \end{aligned} \end{cases}

If the conditions above hold true for integers $m$, $n$, $p$, $q$, and $w$, and $-\log_qw = \dfrac{a}{b}$, where $a$ and $b$ are coprime integers, what is the value of $a^2-b^2$?

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