< Question 2,1.9 Simplify. (13a^7b^9)/(-3a^6)b^(5)

To simplify the given expression:

$$\frac{13a^7b^9}{-3a^6b^5}$$

### Step 1: Simplify the coefficients
The coefficients are $13$ and $-3$. Dividing them gives:
$$\frac{13}{-3} = -\frac{13}{3}.$$

### Step 2: Simplify the powers of $a$
Using the rule of exponents ($\frac{a^m}{a^n} = a^{m-n}$):
$$\frac{a^7}{a^6} = a^{7-6} = a^1 = a.$$

### Step 3: Simplify the powers of $b$
Using the same rule of exponents:
$$\frac{b^9}{b^5} = b^{9-5} = b^4.$$

### Step 4: Combine the results
Now, putting everything together:
$$\frac{13a^7b^9}{-3a^6b^5} = -\frac{13}{3} \cdot a \cdot b^4 = -\frac{13a b^4}{3}.$$

### Final Answer:
$$\boxed{-\frac{13a b^4}{3}}$$