Divide :
`24x^(3)y^(3)` by `-8y^(2)`

Answer

To divide the expression \( 24x^3y^3 \) by \( -8y^2 \), we can follow these steps:

### Step 1: Write the division as a fraction
We can express the division as:
\[ \frac{24x^3y^3}{-8y^2} \]

### Step 2: Separate the constants and variables
We can separate the constants from the variables:
\[ \frac{24}{-8} \cdot \frac{x^3}{1} \cdot \frac{y^3}{y^2} \]

### Step 3: Divide the constants
Now, divide the constants:
\[ \frac{24}{-8} = -3 \]
So, we have:
\[ -3 \cdot \frac{x^3}{1} \cdot \frac{y^3}{y^2} \]

### Step 4: Simplify the variable part
Next, we simplify the variable part. Since \( y^3 \) divided by \( y^2 \) can be simplified by subtracting the exponents (because the bases are the same):
\[ \frac{y^3}{y^2} = y^{3-2} = y^1 = y \]
Thus, we have:
\[ -3x^3y \]

### Step 5: Write the final answer
The final answer after performing the division is:
\[ -3x^3y \]