1. **State the problem:** Simplify the expression $ (9x)(7x+1) $. 2. **Use the distributive property:** Multiply each term inside the parentheses by $9x$. The distributive property states $a(b+c) = ab + ac$. 3. **Apply the property:** $$ (9x)(7x+1) = (9x)(7x) + (9x)(1) $$ 4. **Multiply the terms:** $$ (9x)(7x) = 9 \times 7 \times x \times x = 63x^2 $$ $$ (9x)(1) = 9x $$ 5. **Combine the results:** $$ 63x^2 + 9x $$ 6. **Final answer:** $$ \boxed{63x^2 + 9x} $$