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Express

\log_{\frac{2}{3}} (\frac{2^{\frac{2}{3}} \sqrt[3]{3}}{2})

in a form not involving logarithms.

\frac{2^{\frac{2}{3}} \sqrt[3]{3}}{2} = 2^{- \frac{1}{3}} 3^{\frac{1}{3}}

2^{- \frac{1}{3}} 3^{\frac{1}{3}} = \frac{2^{- \frac{1}{3}}}{3^{- \frac{1}{3}}}

\frac{2^{- \frac{1}{3}}}{3^{- \frac{1}{3}}} = {(\frac{2}{3})}^{- \frac{1}{3}}

If the answer, as a fully simplified fraction, is $\frac{a}{b}$ , give the value of $5 a b$ .