Ответ:

[tex] \frac{7 {x}^{3} }{4 {y}^{2} } \times \frac{216 {x}^{6} }{343 {y}^{3} } \div \frac{18 {x}^{8} }{49 {y}^{4} } = \frac{7 {x}^{3} }{4 {y}^{2} } \frac{4 \times 3 \times 18 {x}^{6} }{7 \times 49 {y}^{3} } \frac{49 {y}^{4} }{18 {x}^{8} } = 3 {x}^{3 + 6 - 8} {y}^{4 - 2 - 3} = \frac{3x}{y} [/tex]

[tex] \frac{ {x}^{3} - 8 }{9 {x}^{2} - 16 } \div \frac{ {x}^{2} + 2x + 4}{3x - 4} = \frac{(x - 2)( {x}^{2} + 2x + 4) }{(3x - 4)(3x + 4)} \frac{3x - 4}{ {x}^{2} + 2x + 4} = \frac{x - 2}{3x + 4} [/tex]

[tex] \frac{x - 2}{ 3x + 4} = \frac{ - 3 - 2}{ - 3 \times 3 + 4} = \frac{5}{5} = 1[/tex]

[tex] \frac{a + 4}{x - a} \div \frac{ab + 4b - 2a - 8}{ex + xy - ae - ay} = \frac{a + 4}{x - a} \frac{(x - a)(e + y)}{(a + 4)(b - 2)} = \frac{e + y}{b - 2} [/tex]