$$\frac{ 3x }{ 4y } \times \frac{ 8y }{ 9x } \div \frac{ { z }^{ 2 } }{ 3 { x }^{ 2 } }$$
$2\times \left(\frac{x}{z}\right)^{2}$
$$\frac{\frac{3x\times 8y}{4y\times 9x}}{\frac{z^{2}}{3x^{2}}}$$
$$\frac{\frac{2}{3}}{\frac{z^{2}}{3x^{2}}}$$
$$\frac{2\times 3x^{2}}{3z^{2}}$$
$$\frac{2x^{2}}{z^{2}}$$
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$\frac{4x}{z^{2}}$
