1. The problem is to find the value of $3^9 - 3^8$. 2. Recall that $3^9 = 3^{8+1} = 3^8 \cdot 3^1$. 3. Substitute this into the expression to get $3^9 - 3^8 = 3^8 \cdot 3 - 3^8$. 4. Factor out $3^8$ from the terms: $3^8 (3 - 1)$. 5. Simplify inside the parentheses: $3 - 1 = 2$. 6. Thus, the expression becomes $3^8 \cdot 2$. 7. Calculate $3^8 = 6561$. 8. Multiply by 2 to get the final answer: $6561 \times 2 = 13122$. Final answer: $13122$.