$$( \frac { 2 } { 3 } ) ^ { - 5 } \times ( \frac { 2 } { 3 } ) ^ { 12 } = ( \frac { 2 } { 3 } ) ^ { 3 m - 2 }$$
$m=3$
$$\left(\frac{2}{3}\right)^{7}=\left(\frac{2}{3}\right)^{3m-2}$$
$$\frac{128}{2187}=\left(\frac{2}{3}\right)^{3m-2}$$
$$\left(\frac{2}{3}\right)^{3m-2}=\frac{128}{2187}$$
$$\log(\left(\frac{2}{3}\right)^{3m-2})=\log(\frac{128}{2187})$$
$$\left(3m-2\right)\log(\frac{2}{3})=\log(\frac{128}{2187})$$
$$3m-2=\frac{\log(\frac{128}{2187})}{\log(\frac{2}{3})}$$
$$3m-2=\log_{\frac{2}{3}}\left(\frac{128}{2187}\right)$$
$$3m=7-\left(-2\right)$$
$$m=\frac{9}{3}$$
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