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Given \( \frac{\log _{2}\left(\frac{\mathrm{b}^{3}}{8}\right)}{\log _{3}\left(\frac{27}{\mathrm{a}^{2}}\right)}=1 \) and \( \log _{3}\left(\frac{9}{\mathrm{a}}\right)=\log _{2}\left(\frac{\mathrm{b}}{4}\right) \). If the largest single digit number which can divide
\( \mathrm{P} \)
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the value of \( \left(\frac{\mathrm{a}}{\mathrm{b}}\right) \) is \( \mathrm{m} \), then find the value of \( \mathrm{m} \).
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