Divide :
`-24x^(4)d` by `-2x^(2)d^`(3)

Answer

To divide the expression \(-24x^4d\) by \(-2x^3d^3\), we can follow these steps:

### Step 1: Write the division as a fraction
We can express the division as:
\[ \frac{-24x^4d}{-2x^3d^3} \]

### Step 2: Simplify the constants
Now, simplify the constant terms:
\[ \frac{-24}{-2} = 12 \]

### Step 3: Simplify the variable \(x\)
Next, simplify the \(x\) terms. When dividing powers with the same base, we subtract the exponents:
\[ \frac{x^4}{x^3} = x^{4-3} = x^1 = x \]

### Step 4: Simplify the variable \(d\)
Now, simplify the \(d\) terms in a similar manner:
\[ \frac{d}{d^3} = d^{1-3} = d^{-2} \]
Since \(d^{-2}\) can be rewritten as \(\frac{1}{d^2}\), we have:
\[ d^{-2} = \frac{1}{d^2} \]

### Step 5: Combine the results
Putting it all together, we have:
\[ \frac{-24x^4d}{-2x^3d^3} = 12 \cdot x \cdot \frac{1}{d^2} = \frac{12x}{d^2} \]

### Final Answer
Thus, the result of dividing \(-24x^4d\) by \(-2x^3d^3\) is:
\[ \frac{12x}{d^2} \]

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