Which Expression Is Equivalent To The One Below?$\frac{(x^2 Y)(x^4 Y^3)}{x Y^2}$A. $\frac{x^8 Y^3}{x Y^2}$ B. $\frac{x^8 Y^3}{x Y^2}$ C. $\frac{x^6 Y^4}{x Y^2}$

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will explore how to simplify a given algebraic expression, and we will use the expression $\frac{(x^2 y)(x^4 y^3)}{x y^2}$ as an example. We will also examine the answer choices and determine which one is equivalent to the given expression.

Understanding the Expression

The given expression is $\frac{(x^2 y)(x^4 y^3)}{x y^2}$. To simplify this expression, we need to apply the rules of exponents and combine like terms.

Step 1: Apply the Product Rule

The product rule states that when we multiply two or more variables with the same base, we add their exponents. In this case, we have $(x^2 y)(x^4 y^3)$. We can apply the product rule to simplify this expression:

$(x^2 y)(x^4 y^3) = x^{2+4} y^{1+3} = x^6 y^4$

Step 2: Simplify the Expression

Now that we have simplified the numerator, we can rewrite the original expression as:

$\frac{x^6 y^4}{x y^2}$

Step 3: Apply the Quotient Rule

The quotient rule states that when we divide two variables with the same base, we subtract their exponents. In this case, we have $\frac{x^6 y^4}{x y^2}$. We can apply the quotient rule to simplify this expression:

$\frac{x^6 y^4}{x y^2} = x^{6-1} y^{4-2} = x^5 y^2$

Conclusion

After simplifying the expression, we get $x^5 y^2$. However, we need to compare this result with the answer choices to determine which one is equivalent to the given expression.

Answer Choices

A. $\frac{x^8 y^3}{x y^2}$ B. $\frac{x^8 y^3}{x y^2}$ C. $\frac{x^6 y^4}{x y^2}$

Which Expression is Equivalent?

To determine which expression is equivalent to the given expression, we need to compare the simplified expression $x^5 y^2$ with the answer choices. We can see that none of the answer choices match the simplified expression. However, we can rewrite the simplified expression as $\frac{x^6 y^4}{x y^2}$, which is equivalent to answer choice C.

Final Answer

Introduction

In our previous article, we explored how to simplify a given algebraic expression, and we used the expression $\frac{(x^2 y)(x^4 y^3)}{x y^2}$ as an example. We also examined the answer choices and determined which one is equivalent to the given expression. In this article, we will provide a Q&A guide to help you better understand how to simplify algebraic expressions.

Q: What is the product rule in algebra?

A: The product rule states that when we multiply two or more variables with the same base, we add their exponents. For example, $(x^2 y)(x^4 y^3) = x^{2+4} y^{1+3} = x^6 y^4$.

Q: How do I apply the product rule?

A: To apply the product rule, simply add the exponents of the variables with the same base. For example, if we have $(x^2 y)(x^4 y^3)$, we would add the exponents of $x$ and $y$ to get $x^6 y^4$.

Q: What is the quotient rule in algebra?

A: The quotient rule states that when we divide two variables with the same base, we subtract their exponents. For example, $\frac{x^6 y^4}{x y^2} = x^{6-1} y^{4-2} = x^5 y^2$.

Q: How do I apply the quotient rule?

A: To apply the quotient rule, simply subtract the exponents of the variables with the same base. For example, if we have $\frac{x^6 y^4}{x y^2}$, we would subtract the exponents of $x$ and $y$ to get $x^5 y^2$.

Q: What is the difference between the product rule and the quotient rule?

A: The product rule is used to multiply variables with the same base, while the quotient rule is used to divide variables with the same base. The product rule adds the exponents, while the quotient rule subtracts the exponents.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you can follow these steps:

1. Apply the product rule to simplify the numerator.
2. Apply the quotient rule to simplify the expression.
3. Combine like terms to simplify the expression further.

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

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

• Forgetting to apply the product rule or the quotient rule.
• Adding or subtracting the wrong exponents.
• Not combining like terms.
• Not simplifying the expression further.

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By understanding the product rule and the quotient rule, and by following the steps outlined in this article, you can simplify even the most complex algebraic expressions. Remember to apply the product rule to simplify the numerator, apply the quotient rule to simplify the expression, and combine like terms to simplify the expression further. With practice and patience, you will become a master of simplifying algebraic expressions.