https://file.aiquickdraw.com/mathbot/file/1729193529276x8bzg5dv.jpg

Let's walk through this problem step-by-step.

### Question:
Simplify:  
\[
(-7x^5)(9x^5)
\]

### Step 1: Group the Coefficients
The coefficients are \(-7\) and \(9\). Multiply these:

\[
-7 \times 9 = -63
\]

### Step 2: Apply the Product Rule of Exponents
The product rule for exponents states:
\[
x^a \cdot x^b = x^{a+b}
\]
Here, both terms have \(x^5\), so:

\[
x^5 \cdot x^5 = x^{5 + 5} = x^{10}
\]

### Step 3: Combine the Results
Now, multiply the coefficient with the variable part:

\[
-63x^{10}
\]

### Final Answer:
\[
\boxed{-63x^{10}}
\]

Let me know if you'd like more details or another example!

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**Related questions for practice:**

1. How would the expression change if the first term was \((-7x^3)\) instead?
2. What happens if the signs of both coefficients were positive?
3. Can the product rule apply if the variables are different, like \(x^5\) and \(y^5\)?
4. What is the general formula for the product of two exponential terms?
5. How do you simplify \((-2x^3)^2\)?

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**Tip:** When multiplying terms with the same base, always add their exponents!

Learn how to simplify the algebraic expression (-7x^5)(9x^5) using exponent rules. The step-by-step guide demonstrates how to multiply coefficients and apply the product rule for exponents. Suitable for students in Grades 8-10.

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