https://file.aiquickdraw.com/mathbot/file/1729229948495sid9uglq.jpg

To solve the given expression \((5x^3)(4x)^3\), let's simplify it step by step:

1. **Simplify the given expression**:
   \[
   (5x^3)(4x)^3
   \]

2. **Apply the power to each term inside the parentheses**:
   \[
   (4x)^3 = 4^3 \cdot x^3 = 64x^3
   \]

3. **Multiply the remaining terms**:
   \[
   5x^3 \cdot 64x^3 = (5 \cdot 64) \cdot (x^3 \cdot x^3)
   \]

4. **Calculate the multiplication**:
   - \( 5 \cdot 64 = 320 \)
   - \( x^3 \cdot x^3 = x^{3+3} = x^6 \)

5. **Combine the results**:
   \[
   320x^6
   \]

So, the expression \((5x^3)(4x)^3\) is equivalent to **320x^6**. The correct answer is:

**320x^6**.

Would you like further details on any part of the solution, or do you have any other questions?

Here are 5 related questions that build on this topic:

1. How do you simplify expressions involving exponents?
2. What are the rules of exponents when multiplying terms with the same base?
3. How do you simplify powers of products like \((ab)^n\)?
4. What is the difference between multiplying powers and raising a power to another power?
5. How would the solution change if the exponents were different, e.g., \((5x^2)(4x)^4\)?

**Tip:** When raising a product to a power, apply the exponent to each part separately before multiplying the results.

Which expression is equivalent to (5x^3)(4x)^3?

Learn how to simplify the expression (5x^3)(4x)^3 using exponent rules. This step-by-step guide breaks down the multiplication of polynomials and exponentiation. 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