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Algebra Level 2

m×a×t=18m×a×h=32m×t×h=13a×t×h=162 \begin{aligned} m\times a\times t & =& \frac {1}{8} \\ m\times a\times h & =& 32 \\ m\times t\times h & =& \frac{1}{3} \\ a\times t\times h & =& 162 \\ \end{aligned}

Given that m,a,t,hm,a,t,h are elements of real numbers that satisfy the equations above. Find the value of m×a×t×hm\times a\times t\times h.


See part 2 here and part 4 here.
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