$$( \frac { 6 } { 7 } ) ^ { 7 } \times ( \frac { 5 } { 6 } ) ^ { 7 } = ( \frac { 5 } { 7 } ) ^ { 7 }$$
$\text{true}$
$$\frac{279936}{823543}\times \left(\frac{5}{6}\right)^{7}=\left(\frac{5}{7}\right)^{7}$$
$$\frac{279936}{823543}\times \frac{78125}{279936}=\left(\frac{5}{7}\right)^{7}$$
$$\frac{279936\times 78125}{823543\times 279936}=\left(\frac{5}{7}\right)^{7}$$
$$\frac{78125}{823543}=\left(\frac{5}{7}\right)^{7}$$
$$\frac{78125}{823543}=\frac{78125}{823543}$$
$$\text{true}$$
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