$$(\frac{2}{3})^{3}\times(\frac{4}{7})^{5}\times\frac{3^{3}\times7^{10}}{2^{13}}$$
$16807$
$$\frac{8}{27}\times \left(\frac{4}{7}\right)^{5}\times \frac{3^{3}\times 7^{10}}{2^{13}}$$
$$\frac{8}{27}\times \frac{1024}{16807}\times \frac{3^{3}\times 7^{10}}{2^{13}}$$
$$\frac{8\times 1024}{27\times 16807}\times \frac{3^{3}\times 7^{10}}{2^{13}}$$
$$\frac{8192}{453789}\times \frac{3^{3}\times 7^{10}}{2^{13}}$$
$$\frac{8192}{453789}\times \frac{27\times 7^{10}}{2^{13}}$$
$$\frac{8192}{453789}\times \frac{27\times 282475249}{2^{13}}$$
$$\frac{8192}{453789}\times \frac{7626831723}{2^{13}}$$
$$\frac{8192}{453789}\times \frac{7626831723}{8192}$$
$$\frac{8192\times 7626831723}{453789\times 8192}$$
$$\frac{7626831723}{453789}$$
$$16807$$
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$7^{5}$
