1. **State the problem:** Find how many trailing zeroes are in the product $$650 \times 4^6 \times 5^9$$. 2. **Recall the rule for trailing zeroes:** Trailing zeroes in a number come from factors of 10, and each 10 is made from one 2 and one 5. 3. **Prime factorize each part:** - 650 = $2 \times 5^2 \times 13$ - $4^6 = (2^2)^6 = 2^{12}$ - $5^9$ is already prime factors of 5. 4. **Combine all factors:** $$650 \times 4^6 \times 5^9 = (2 \times 5^2 \times 13) \times 2^{12} \times 5^9 = 2^{1+12} \times 5^{2+9} \times 13 = 2^{13} \times 5^{11} \times 13$$ 5. **Count pairs of 2 and 5:** The number of trailing zeroes is the minimum of the exponents of 2 and 5. - Number of 2s = 13 - Number of 5s = 11 6. **Result:** The number of trailing zeroes is $$\min(13, 11) = 11$$. **Final answer:** 11 trailing zeroes.