b) \( \left(\frac{3}{5}\right)^{3} \times\left(\frac{2}{3}\right)^{2} \times\left(\frac{5}{7}\right)^{2} \)

To simplify the expression \( \left(\frac{3}{5}\right)^{3} \times \left(\frac{2}{3}\right)^{2} \times \left(\frac{5}{7}\right)^{2} \), we first calculate each part individually: 1. \( \left(\frac{3}{5}\right)^{3} = \frac{27}{125} \) 2. \( \left(\frac{2}{3}\right)^{2} = \frac{4}{9} \) 3. \( \left(\frac{5}{7}\right)^{2} = \frac{25}{49} \) Now, combine these fractions: \[ \frac{27}{125} \times \frac{4}{9} \times \frac{25}{49} \] Next, multiply the numerators together: \[ 27 \times 4 \times 25 = 2700 \] And multiply the denominators together: \[ 125 \times 9 \times 49 = 54925 \] So, we have: \[ \frac{2700}{54925} \] Now, it is often helpful to simplify this fraction. We can divide the numerator and denominator by their greatest common divisor (GCD). The GCD of 2700 and 54925 is 25, which simplifies the fraction to: \[ \frac{108}{2197} \] Thus, the final answer for the expression is: \[ \frac{108}{2197} \]