$$\frac{4}{5}\times6\frac{7}{9}\times10\frac{8}{10}\times7$$
$\frac{10248}{25}=409.92$
$$\frac{4}{5}\times \frac{54+7}{9}\times \frac{10\times 10+8}{10}\times 7$$
$$\frac{4}{5}\times \frac{61}{9}\times \frac{10\times 10+8}{10}\times 7$$
$$\frac{4\times 61}{5\times 9}\times \frac{10\times 10+8}{10}\times 7$$
$$\frac{244}{45}\times \frac{10\times 10+8}{10}\times 7$$
$$\frac{244}{45}\times \frac{100+8}{10}\times 7$$
$$\frac{244}{45}\times \frac{108}{10}\times 7$$
$$\frac{244}{45}\times \frac{54}{5}\times 7$$
$$\frac{244\times 54}{45\times 5}\times 7$$
$$\frac{13176}{225}\times 7$$
$$\frac{1464}{25}\times 7$$
$$\frac{1464\times 7}{25}$$
$$\frac{10248}{25}$$
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$\frac{2 ^ {3} \cdot 3 \cdot 7 \cdot 61}{5 ^ {2}} = 409\frac{23}{25} = 409.92$
