Answer:

[tex]\sf \green { \therefore \: \frac{ {6}^{4} \times {9}^{2} \times 125}{ {3}^{2} \times {4}^{2} \times {5}^{3} } = 729}[/tex]

Step-by-step explanation:

[tex] \sf \frac{ {6}^{4} \times {9}^{2} \times 125}{ {3}^{2} \times {4}^{2} \times {5}^{3} } = \frac{ {6}^{4} \times {9}^{2} \times \cancel{125}}{ ({3 \times 4})^{2} \times \cancel{125}} [/tex]

[tex] \sf \frac{ {6}^{4} \times {9}^{2} }{ {12}^{2} } = {6}^{4} \times { (\frac{ \cancel9^{ \: 3} }{ \cancel{12}_{ \: 4}}) }^{2} = {6}^{4} \times {( \frac{3}{4}) }^{2} [/tex]

[tex] \sf 6 \times 6 \times 6 \times 6 \times \frac{3}{4} \times \frac{3}{4}[/tex]

[tex] \sf 1296 \times ( \frac{3 \times 3}{4 \times 4} ) = 1296 \times \frac{9}{16} [/tex]

[tex] \sf \frac{^{81 \: } \cancel{1296}}{1} \times \frac{9}{ \cancel{16}_{ \: 1}} = 81 \times 9 = 729[/tex]