Divide :
`15a^(4)b` by `-5a^(3)b`

Answer

To solve the problem of dividing \( 15a^4b \) by \( -5a^3b \), we can follow these steps:

### Step 1: Write the division as a fraction
We start by expressing the division as a fraction:
\[ \frac{15a^4b}{-5a^3b} \]

### Step 2: Separate the constant and variable terms
We can separate the constant terms and the variable terms:
\[ \frac{15}{-5} \cdot \frac{a^4}{a^3} \cdot \frac{b}{b} \]

### Step 3: Simplify the constant terms
Now, simplify the constant term:
\[ \frac{15}{-5} = -3 \]

### Step 4: Simplify the variable terms
Next, we simplify the variable terms. For \( a^4 \) and \( a^3 \):
\[ \frac{a^4}{a^3} = a^{4-3} = a^1 = a \]
And for \( b \) in the numerator and denominator:
\[ \frac{b}{b} = 1 \quad (\text{since } b \neq 0) \]

### Step 5: Combine the results
Putting it all together, we have:
\[ -3 \cdot a \cdot 1 = -3a \]

### Final Answer
Thus, the result of dividing \( 15a^4b \) by \( -5a^3b \) is:
\[ \boxed{-3a} \]