1. The problem is to simplify the expression $$7000\left(1-\left[\frac{1+0.12}{1+0.15}\right]^{\frac{9}{0.15-0.12}}\right)$$. 2. First, calculate the base inside the brackets: $$\frac{1+0.12}{1+0.15} = \frac{1.12}{1.15} \approx 0.9739$$. 3. Next, calculate the exponent denominator: $$0.15 - 0.12 = 0.03$$. 4. The exponent is then $$\frac{9}{0.03} = 300$$. 5. Raise the base to the power of the exponent: $$0.9739^{300}$$. 6. Calculate $$0.9739^{300}$$ using logarithms or a calculator: $$\ln(0.9739) \approx -0.0264$$ $$-0.0264 \times 300 = -7.92$$ $$e^{-7.92} \approx 0.00036$$. 7. Substitute back into the expression: $$7000 \times (1 - 0.00036) = 7000 \times 0.99964 = 6997.48$$. 8. Final answer: $$\boxed{6997.48}$$. This means the value of the original expression is approximately 6997.48.