https://file.aiquickdraw.com/mathbot/file/172565489260204h5fb31.jpg

The expression in the image is:

\[
(-pq^5)(-5p^{3-x}q^2)
\]

Let's simplify this step by step:

### Step 1: Multiply the constants and signs
The signs are both negative, so multiplying two negative terms will give a positive result:
\[
(-1)(-1) = 1
\]

The constants (if any) are \(-5\), so the product of the constants is:
\[
1 \times (-5) = 5
\]

### Step 2: Apply the product of powers rule
For the variables, we use the property of exponents:
\[
p^a \cdot p^b = p^{a + b}, \quad q^a \cdot q^b = q^{a + b}
\]

Now, we can apply this to both \(p\) and \(q\):

- For \(p\):
\[
p^1 \cdot p^{3-x} = p^{1 + (3 - x)} = p^{4 - x}
\]

- For \(q\):
\[
q^5 \cdot q^2 = q^{5 + 2} = q^7
\]

### Step 3: Combine the results
Putting everything together, we get:
\[
5p^{4 - x}q^7
\]

This is the simplified expression.

Would you like further details or have any questions?

Here are some related questions:
1. How do you simplify expressions with negative exponents?
2. What are the rules for multiplying powers with the same base?
3. How do you handle variables with unknown exponents like \(x\) in multiplication?
4. What happens if the base of the terms being multiplied are different?
5. How do you factor a polynomial expression involving exponents?

**Tip:** When multiplying terms with exponents, always remember to add the exponents of like bases.

Explore how to simplify the algebraic expression (-pq^5)(-5p^{3-x}q^2) step-by-step, focusing on exponentiation, multiplication of polynomials, and the product of powers rule. Ideal for students in Grades 9-11.

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