What Is The Product? { (4x)(-3x 8)(-7x 3)$}$A. { -84x^{12}$}$ B. { -84x^{24}$}$ C. ${ 84x^{12}\$} D. ${ 84x^{24}\$}

When it comes to multiplying algebraic expressions, it's essential to understand the rules of exponents and how to apply them correctly. In this article, we will explore the product of the given expression $(4x)(-3x8)(-7x3)$ and determine the correct answer among the options provided.

Understanding the Rules of Exponents

Before we dive into the product of the given expression, let's review the rules of exponents. When multiplying variables with the same base, we add their exponents. For example, $x^a \cdot x^b = x^{a+b}$. However, when multiplying variables with different bases, we multiply the coefficients and add the exponents. For instance, $x^a \cdot y^b = x^a \cdot y^b$.

Applying the Rules of Exponents to the Given Expression

Now that we have reviewed the rules of exponents, let's apply them to the given expression $(4x)(-3x^8)(-7x^3)$. To find the product, we will multiply the coefficients and add the exponents.

Step 1: Multiply the Coefficients

The coefficients of the given expression are 4, -3, and -7. To find the product of the coefficients, we multiply them together:

$4 \cdot -3 \cdot -7 = 84$

Step 2: Add the Exponents

The exponents of the given expression are 1, 8, and 3. To find the product of the exponents, we add them together:

$1 + 8 + 3 = 12$

Step 3: Write the Product

Now that we have multiplied the coefficients and added the exponents, we can write the product of the given expression:

$(4x)(-3x^8)(-7x^3) = 84x^{12}$

Evaluating the Options

Now that we have found the product of the given expression, let's evaluate the options provided:

A. $-84x^{12}$ B. $-84x^{24}$ C. $84x^{12}$ D. $84x^{24}$

Based on our calculation, the correct answer is:

C. $84x^{12}$

Conclusion

In this article, we explored the product of the given expression $(4x)(-3x^8)(-7x^3)$ and determined the correct answer among the options provided. By applying the rules of exponents, we were able to multiply the coefficients and add the exponents to find the product. We also evaluated the options and determined that the correct answer is C. $84x^{12}$.

Frequently Asked Questions

• What is the product of the given expression $(4x)(-3x^8)(-7x^3)$?
• How do we apply the rules of exponents to multiply variables with the same base?
• What is the correct answer among the options provided?

Answer

• The product of the given expression is $84x^{12}$.
• To apply the rules of exponents, we add the exponents when multiplying variables with the same base.
• The correct answer among the options provided is C. $84x^{12}$.
  Frequently Asked Questions (FAQs) About the Product of Algebraic Expressions ================================================================================

In our previous article, we explored the product of the given expression $(4x)(-3x^8)(-7x^3)$ and determined the correct answer among the options provided. However, we understand that there may be more questions and concerns about the topic. In this article, we will address some of the frequently asked questions (FAQs) about the product of algebraic expressions.

Q: What is the product of two or more algebraic expressions?

A: The product of two or more algebraic expressions is the result of multiplying them together. When multiplying algebraic expressions, we multiply the coefficients and add the exponents.

Q: How do I multiply algebraic expressions with the same base?

A: When multiplying algebraic expressions with the same base, we add their exponents. For example, $x^a \cdot x^b = x^{a+b}$.

Q: How do I multiply algebraic expressions with different bases?

A: When multiplying algebraic expressions with different bases, we multiply the coefficients and add the exponents. For instance, $x^a \cdot y^b = x^a \cdot y^b$.

Q: What is the rule for multiplying negative numbers?

A: When multiplying negative numbers, we multiply the absolute values of the numbers and then apply the rule for multiplying positive numbers. If the product of the absolute values is positive, the result is negative. If the product of the absolute values is negative, the result is positive.

Q: How do I simplify the product of algebraic expressions?

A: To simplify the product of algebraic expressions, we can combine like terms and apply the rules of exponents. For example, $(x^2 + 3x)(x^2 - 2x) = x^4 - 2x^3 + 3x^3 - 6x = x^4 + x^3 - 6x$.

Q: What are some common mistakes to avoid when multiplying algebraic expressions?

A: Some common mistakes to avoid when multiplying algebraic expressions include:

• Forgetting to multiply the coefficients
• Forgetting to add the exponents
• Not simplifying the product
• Not applying the rules of exponents correctly

Q: How can I practice multiplying algebraic expressions?

A: You can practice multiplying algebraic expressions by working through examples and exercises. You can also use online resources and practice tests to help you improve your skills.

Q: What are some real-world applications of multiplying algebraic expressions?

A: Multiplying algebraic expressions has many real-world applications, including:

• Calculating the area and perimeter of shapes
• Determining the volume of 3D objects
• Modeling population growth and decay
• Solving systems of equations

Conclusion

In this article, we addressed some of the frequently asked questions (FAQs) about the product of algebraic expressions. We hope that this article has provided you with a better understanding of the topic and has helped you to improve your skills. If you have any further questions or concerns, please don't hesitate to ask.

Additional Resources

• Khan Academy: Algebra
• Mathway: Algebra Calculator
• Wolfram Alpha: Algebra Solver

Related Articles

• What is the Product of the Given Expression?
• Understanding the Rules of Exponents
• Applying the Rules of Exponents to the Given Expression