1. **State the problem:** Simplify the expression $$\left(\frac{4}{-9}\right) \times \left(\frac{-21}{-32}\right) \times \left(\frac{-3}{14}\right)$$. 2. **Rewrite the expression:** $$\frac{4}{-9} \times \frac{-21}{-32} \times \frac{-3}{14}$$ 3. **Simplify signs:** Note that $$\frac{4}{-9} = -\frac{4}{9}$$ and $$\frac{-21}{-32} = \frac{21}{32}$$ (negative divided by negative is positive), and $$\frac{-3}{14} = -\frac{3}{14}$$. So the expression becomes: $$-\frac{4}{9} \times \frac{21}{32} \times -\frac{3}{14}$$ 4. **Multiply the numerators and denominators:** $$\frac{-4 \times 21 \times -3}{9 \times 32 \times 14}$$ 5. **Simplify the negatives:** $$-4 \times 21 \times -3 = (-4) \times 21 \times (-3) = 4 \times 21 \times 3 = 252$$ So numerator is 252. 6. **Calculate denominator:** $$9 \times 32 = 288$$ $$288 \times 14 = 4032$$ So denominator is 4032. 7. **Write the fraction:** $$\frac{252}{4032}$$ 8. **Simplify the fraction:** Find the greatest common divisor (GCD) of 252 and 4032. 252 factors: $$2^2 \times 3^2 \times 7$$ 4032 factors: $$2^6 \times 3^2 \times 7$$ GCD is $$2^2 \times 3^2 \times 7 = 252$$ 9. **Divide numerator and denominator by 252:** $$\frac{\cancel{252}^{1}}{\cancel{4032}^{16}}$$ 10. **Final simplified answer:** $$\frac{1}{16}$$