12. Simplify the expression: \( \left(5 x^{6}\right)\left(3 x^{-2}\right) \)

To simplify the expression \( \left(5 x^{6}\right)\left(3 x^{-2}\right) \), follow these steps: 1. **Multiply the coefficients (constants) together:** \[ 5 \times 3 = 15 \] 2. **Apply the laws of exponents to multiply the \( x \) terms:** \[ x^{6} \times x^{-2} = x^{6 + (-2)} = x^{4} \] This is based on the exponent rule: \[ a^{m} \times a^{n} = a^{m+n} \] 3. **Combine the results from steps 1 and 2:** \[ 15 \times x^{4} = 15x^{4} \] **Final Simplified Expression:** \[ 15x^{4} \]