Divide
`-24p^(5)q^(2) " by " 16pq^(4)`

Answer

To solve the problem of dividing \(-24p^{5}q^{2}\) by \(16pq^{4}\), we can follow these steps:

### Step 1: Write the division as a fraction
We start by expressing the division as a fraction:
\[ \frac{-24p^{5}q^{2}}{16pq^{4}} \]

**Hint:** Remember that division can be represented as a fraction.

### Step 2: Simplify the coefficients
Next, we simplify the coefficients \(-24\) and \(16\). We can find the greatest common divisor (GCD) of these numbers:
\[ \frac{-24}{16} = \frac{-3}{2} \]

**Hint:** Look for the GCD to simplify the numerical part of the fraction.

### Step 3: Simplify the variable \(p\)
Now, we simplify the \(p\) terms. We have \(p^{5}\) in the numerator and \(p\) in the denominator:
\[ \frac{p^{5}}{p} = p^{5-1} = p^{4} \]

**Hint:** When dividing like bases, subtract the exponents.

### Step 4: Simplify the variable \(q\)
Next, we simplify the \(q\) terms. We have \(q^{2}\) in the numerator and \(q^{4}\) in the denominator:
\[ \frac{q^{2}}{q^{4}} = q^{2-4} = q^{-2} \]

**Hint:** Again, subtract the exponents when dividing like bases.

### Step 5: Combine the results
Now we can combine all the simplified parts together:
\[ \frac{-3}{2} \cdot p^{4} \cdot q^{-2} \]
This can also be written as:
\[ -\frac{3}{2} p^{4} \cdot \frac{1}{q^{2}} = -\frac{3p^{4}}{2q^{2}} \]

**Hint:** Remember that \(q^{-2}\) can be expressed as \(\frac{1}{q^{2}}\).

### Final Answer
Thus, the final answer is:
\[ -\frac{3p^{4}}{2q^{2}} \]

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