1. **State the problem:** Multiply and simplify the expression $2x \cdot 3y^9 \cdot 7x^5y^3$. 2. **Write the expression:** $$2x \times 3y^9 \times 7x^5y^3$$ 3. **Multiply the coefficients (numbers):** $$2 \times 3 \times 7 = 42$$ 4. **Multiply the variables with the same base by adding their exponents:** - For $x$: $x^{1} \times x^{5} = x^{1+5} = x^{6}$ - For $y$: $y^{9} \times y^{3} = y^{9+3} = y^{12}$ 5. **Combine all parts:** $$42x^{6}y^{12}$$ 6. **Final simplified answer:** $$\boxed{42x^{6}y^{12}}$$