Interesting logarithms - 1

Algebra Level 2

{logmw=12lognw=16logpw=36logmnpqw=72\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 mm, nn, pp, qq, and ww, and logqw=ab-\log_qw = \dfrac{a}{b}, where aa and bb are coprime integers, what is the value of a2b2a^2-b^2?

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