b) \( \left(\frac{-3}{5}\right)^{14} \times\left(\frac{-3}{5}\right)^{-3}=\left(\frac{-3}{5}\right)^{3 m+2} \)

To solve the equation \( \left(\frac{-3}{5}\right)^{14} \times\left(\frac{-3}{5}\right)^{-3} = \left(\frac{-3}{5}\right)^{3m+2} \), we will first simplify the left-hand side using the rule of exponents that states \( a^m \times a^n = a^{m+n} \). 1. Combine the exponents on the left side: \[ \left(\frac{-3}{5}\right)^{14 + (-3)} = \left(\frac{-3}{5}\right)^{14 - 3} = \left(\frac{-3}{5}\right)^{11} \] 2. Now, we can equate the exponents: \[ 11 = 3m + 2 \] 3. To solve for \( m \), subtract 2 from both sides: \[ 11 - 2 = 3m \implies 9 = 3m \] 4. Divide both sides by 3: \[ m = 3 \] Thus, the solution is \( m = 3 \).