1. **State the problem:** Simplify the expression $$\frac{-3xy^4}{-21x^3y^2}$$. 2. **Write the expression:** $$\frac{-3xy^4}{-21x^3y^2}$$. 3. **Simplify the coefficients:** Both numerator and denominator have negative signs which cancel out: $$\frac{\cancel{-}3xy^4}{\cancel{-}21x^3y^2} = \frac{3xy^4}{21x^3y^2}$$. 4. **Simplify the numerical fraction:** $$\frac{3}{21} = \frac{\cancel{3}^1}{\cancel{21}_7} = \frac{1}{7}$$. 5. **Simplify the variables:** - For $x$: $$\frac{x}{x^3} = \frac{\cancel{x}^1}{x^{\cancel{3}}_2} = \frac{1}{x^2} = x^{-2}$$. - For $y$: $$\frac{y^4}{y^2} = y^{4-2} = y^2$$. 6. **Combine all simplified parts:** $$\frac{1}{7} \times x^{-2} \times y^2 = \frac{y^2}{7x^2}$$. **Final answer:** $$\frac{y^2}{7x^2}$$.