`(8a^(2)b^(3) )/ (-2ab) = ?`

Options

A. `4ab^(2)`
B. `4a^(2)b`
C. `-4ab^(2)`
D. `-4a^(2) b`

Answer

To solve the expression \((8a^{2}b^{3}) / (-2ab)\), we will follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \frac{8a^{2}b^{3}}{-2ab} \]

### Step 2: Divide the coefficients
First, we divide the numerical coefficients:
\[ \frac{8}{-2} = -4 \]

### Step 3: Apply the laws of exponents for \(a\)
Next, we apply the laws of exponents for the variable \(a\):
\[ \frac{a^{2}}{a} = a^{2-1} = a^{1} = a \]

### Step 4: Apply the laws of exponents for \(b\)
Now, we apply the laws of exponents for the variable \(b\):
\[ \frac{b^{3}}{b} = b^{3-1} = b^{2} \]

### Step 5: Combine the results
Now, we combine all the results from the previous steps:
\[ -4 \cdot a \cdot b^{2} = -4ab^{2} \]

### Final Answer
Thus, the final answer is:
\[ \frac{8a^{2}b^{3}}{-2ab} = -4ab^{2} \]

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