$$( \frac { 2 } { 7 } ) ^ { - 3 } \times ( \frac { 2 } { 7 } ) ^ { 10 } = ( \frac { 2 } { 7 } ) ^ { 3 m + 1 }$$
$m=2$
$$\left(\frac{2}{7}\right)^{7}=\left(\frac{2}{7}\right)^{3m+1}$$
$$\frac{128}{823543}=\left(\frac{2}{7}\right)^{3m+1}$$
$$\left(\frac{2}{7}\right)^{3m+1}=\frac{128}{823543}$$
$$\log(\left(\frac{2}{7}\right)^{3m+1})=\log(\frac{128}{823543})$$
$$\left(3m+1\right)\log(\frac{2}{7})=\log(\frac{128}{823543})$$
$$3m+1=\frac{\log(\frac{128}{823543})}{\log(\frac{2}{7})}$$
$$3m+1=\log_{\frac{2}{7}}\left(\frac{128}{823543}\right)$$
$$3m=7-1$$
$$m=\frac{6}{3}$$
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