1. **Stating the problem:** Simplify the expression $ \frac{8x9z6}{7^4 + z} $. 2. **Understanding the expression:** The numerator is $8 \times 9 \times z \times 6$ and the denominator is $7^4 + z$. 3. **Calculate the numerator:** $$8 \times 9 = 72$$ $$72 \times 6 = 432$$ So, numerator = $$432z$$. 4. **Calculate the denominator:** $$7^4 = 7 \times 7 \times 7 \times 7 = 2401$$ So, denominator = $$2401 + z$$. 5. **Write the simplified expression:** $$\frac{432z}{2401 + z}$$ 6. **Final answer:** The simplified form of the expression is $$\frac{432z}{2401 + z}$$.