https://r2.erweima.ai/mathbot/image/17271986742501u0kze9k.jpg

The expression you provided is:

\[
2x^5 \cdot 3v^7 \cdot x^5 \cdot 2v
\]

To simplify this multiplication:

### Step 1: Group like terms
We can group the constants, the powers of \(x\), and the powers of \(v\) separately.

\[
(2 \cdot 3 \cdot 2) \cdot (x^5 \cdot x^5) \cdot (v^7 \cdot v)
\]

### Step 2: Multiply the constants
\[
2 \cdot 3 \cdot 2 = 12
\]

### Step 3: Apply the product of powers rule for the variables
- For \(x\), we use the rule \(x^a \cdot x^b = x^{a+b}\):
  \[
  x^5 \cdot x^5 = x^{5+5} = x^{10}
  \]
  
- For \(v\), similarly:
  \[
  v^7 \cdot v = v^{7+1} = v^8
  \]

### Step 4: Combine everything
\[
12 \cdot x^{10} \cdot v^8
\]

So, the simplified expression is:

\[
12x^{10}v^8
\]

Would you like further clarification or more details?

Here are some related questions you might find helpful:
1. How do you multiply expressions with different variables?
2. What is the rule for multiplying powers of the same base?
3. How do you simplify expressions involving exponents?
4. What happens when you multiply constants with variables?
5. How does this multiplication compare to dividing expressions with exponents?

**Tip**: Always simplify constants first when multiplying terms in algebraic expressions—it makes the rest of the problem easier to manage.

Multiplicar: \(2x^5 \cdot 3v^7 \cdot x^5 \cdot 2v\)

Learn how to simplify the algebraic expression \(2x^5 \cdot 3v^7 \cdot x^5 \cdot 2v\) by multiplying like terms and applying the product of powers rule. This step-by-step guide is ideal for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation