To solve the expression \(-u^5 \cdot (-4u^5)\), we will apply the following steps:

### Step 1: Multiply the coefficients
The coefficients in this expression are \(-1\) (from \(-u^5\)) and \(-4\). Multiplying these gives:
\[
-1 \cdot (-4) = 4
\]

### Step 2: Multiply the variables
The variables are both \(u^5\). Using the product rule of exponents, which states that \(a^m \cdot a^n = a^{m+n}\), we add the exponents:
\[
u^5 \cdot u^5 = u^{5+5} = u^{10}
\]

### Step 3: Combine the results
Multiplying the coefficients and variables together, we get:
\[
4u^{10}
\]

### Final Answer:
\[
4u^{10}
\]

Would you like more details or have any questions? Here are some related questions to deepen your understanding:

1. What is the product rule for exponents and how does it apply to different bases?
2. How does multiplying negative numbers work in general?
3. How would the expression change if one of the exponents was different, like \(u^5 \cdot u^3\)?
4. What happens if the coefficient was a fraction or a decimal, like \(-u^5 \cdot (-0.5u^5)\)?
5. How would you handle this expression if there were additional terms, like \(-u^5 (-4u^5 + 2u^3)\)?

**Tip:** When multiplying powers with the same base, always remember to add the exponents!

Learn how to solve the expression -u^5 * (-4u^5) using the product rule for exponents and the multiplication of negative coefficients. This problem covers essential concepts of exponents and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation