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Let's break them down:

### Problem 1:
The expression is:

\[
(u^7 v)(9v^4)
\]

**Solution:**
1. Apply the multiplication rule for exponents. The variables with the same base should have their exponents added. Here, we have \(v\) in both terms:
   \[
   u^7 \cdot v \cdot 9 \cdot v^4
   \]
2. Combine the terms:
   \[
   u^7 \cdot 9 \cdot v^{1 + 4}
   \]
   which simplifies to:
   \[
   9u^7v^5
   \]

So, the simplified expression is:
\[
9u^7v^5
\]

---

### Problem 2:
The expression is:

\[
-9(v^4)^2
\]

**Solution:**
1. Apply the power of a power rule, which states that when you raise a power to another power, you multiply the exponents:
   \[
   (v^4)^2 = v^{4 \times 2} = v^8
   \]
2. Now multiply by \(-9\):
   \[
   -9v^8
   \]

So, the simplified expression is:
\[
-9v^8
\]

---

Would you like any more details on these solutions or have any further questions?

Here are 5 related questions for practice:
1. How do you simplify \((x^3)(4x^5)\)?
2. Simplify \((-2y^3)(5y^6)\).
3. Simplify \((3a^2b^4)(2ab^3)\).
4. How do you simplify \((5x^2y^3)^2\)?
5. Simplify \(-4(z^5)^3\).

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

Learn how to simplify expressions like (u^7 * v)(9v^4) and -9(v^4)^2 by applying the rules of exponents. This problem covers key algebraic concepts such as the power of a power rule and multiplication of terms with the same base. Suitable for students in Grades 8-10.

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