\( \frac{\frac{9 z^{3} x^{5}}{49}}{\frac{63 x^{2} z^{5}}{35}} \) simplify

To simplify the expression \( \frac{\frac{9 z^{3} x^{5}}{49}}{\frac{63 x^{2} z^{5}}{35}} \), you start by multiplying by the reciprocal of the denominator: \[ \frac{9 z^{3} x^{5}}{49} \times \frac{35}{63 x^{2} z^{5}}. \] Now, simplify the coefficients and variables: 1. **Coefficients:** \[ \frac{9 \times 35}{49 \times 63} = \frac{315}{3087}. \] By dividing both the numerator and the denominator by 9, you get: \[ \frac{35}{343}. \] 2. **Variables:** For the variable \( x \): \[ x^{5} / x^{2} = x^{5-2} = x^{3}. \] For the variable \( z \): \[ z^{3} / z^{5} = z^{3-5} = z^{-2} = \frac{1}{z^{2}}. \] Putting it all together, you have: \[ \frac{35 x^{3}}{343 z^{2}}. \] Finally, simplify this: \[ \frac{5 x^{3}}{49 z^{2}}. \] So, the simplified expression is: \[ \frac{5 x^{3}}{49 z^{2}}. \]