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

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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 the process of simplifying algebraic expressions, with a focus on the given expression: (x2y)(x4y3)xy2\frac{\left(x^2 y\right)\left(x^4 y^3\right)}{x y^2}. We will examine the different options provided and determine which one is equivalent to the given expression.

Understanding the Given Expression

The given expression is (x2y)(x4y3)xy2\frac{\left(x^2 y\right)\left(x^4 y^3\right)}{x y^2}. To simplify this expression, we need to apply the rules of exponents and follow the order of operations (PEMDAS).

Applying the Rules of Exponents

The rules of exponents state that when multiplying two numbers with the same base, we add their exponents. In this case, we have:

(x2y)(x4y3)=x2+4y1+3=x6y4\left(x^2 y\right)\left(x^4 y^3\right) = x^{2+4} y^{1+3} = x^6 y^4

Simplifying the Expression

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

x6y4xy2\frac{x^6 y^4}{x y^2}

Examining the Options

We are given three options to choose from:

A. x6y3xy2\frac{x^6 y^3}{x y^2} B. x8y3xy2\frac{x^8 y^3}{x y^2} C. x6y4xy2\frac{x^6 y^4}{x y^2}

Analyzing Option A

Option A is x6y3xy2\frac{x^6 y^3}{x y^2}. To determine if this option is equivalent to the given expression, we need to simplify it:

x6y3xy2=x6−1y3−2=x5y1\frac{x^6 y^3}{x y^2} = x^{6-1} y^{3-2} = x^5 y^1

This option is not equivalent to the given expression.

Analyzing Option B

Option B is x8y3xy2\frac{x^8 y^3}{x y^2}. To determine if this option is equivalent to the given expression, we need to simplify it:

x8y3xy2=x8−1y3−2=x7y1\frac{x^8 y^3}{x y^2} = x^{8-1} y^{3-2} = x^7 y^1

This option is not equivalent to the given expression.

Analyzing Option C

Option C is x6y4xy2\frac{x^6 y^4}{x y^2}. To determine if this option is equivalent to the given expression, we need to simplify it:

x6y4xy2=x6−1y4−2=x5y2\frac{x^6 y^4}{x y^2} = x^{6-1} y^{4-2} = x^5 y^2

This option is not equivalent to the given expression.

Conclusion

After analyzing all the options, we can conclude that none of them are equivalent to the given expression. However, we can see that the given expression can be simplified to:

x6y4xy2=x6−1y4−2=x5y2\frac{x^6 y^4}{x y^2} = x^{6-1} y^{4-2} = x^5 y^2

This is not one of the options provided, but it is the correct simplification of the given expression.

Final Answer

The final answer is not among the options provided. However, the correct simplification of the given expression is:

x6y4xy2=x5y2\frac{x^6 y^4}{x y^2} = x^5 y^2

This is the correct answer.

Frequently Asked Questions

Q: What is the given expression?

A: The given expression is (x2y)(x4y3)xy2\frac{\left(x^2 y\right)\left(x^4 y^3\right)}{x y^2}.

Q: How do we simplify the given expression?

A: To simplify the given expression, we need to apply the rules of exponents and follow the order of operations (PEMDAS).

Q: What are the options provided?

A: The options provided are:

A. x6y3xy2\frac{x^6 y^3}{x y^2} B. x8y3xy2\frac{x^8 y^3}{x y^2} C. x6y4xy2\frac{x^6 y^4}{x y^2}

Q: Which option is equivalent to the given expression?

A: None of the options provided are equivalent to the given expression.

Q: What is the correct simplification of the given expression?

A: The correct simplification of the given expression is x6y4xy2=x5y2\frac{x^6 y^4}{x y^2} = x^5 y^2.

References

Note: The references provided are for general information and are not specific to the given problem.

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and understanding them is essential for success in math and science. In this article, we will provide a comprehensive Q&A guide to help you better understand algebraic expressions.

Q&A

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations.

Q: What are the basic components of an algebraic expression?

A: The basic components of an algebraic expression are:

  • Variables: Letters or symbols that represent unknown values.
  • Constants: Numbers that do not change value.
  • Mathematical operations: Addition, subtraction, multiplication, and division.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to apply the rules of exponents and follow the order of operations (PEMDAS).

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when simplifying an algebraic expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next.
  • Multiplication and Division: Evaluate multiplication and division operations from left to right.
  • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I apply the rules of exponents?

A: The rules of exponents state that when multiplying two numbers with the same base, you add their exponents. For example:

  • x2â‹…x3=x2+3=x5x^2 \cdot x^3 = x^{2+3} = x^5

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents an unknown value, while a constant is a number that does not change value.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the values of the variables and perform the mathematical operations.

Q: What is the importance of algebraic expressions in real-life situations?

A: Algebraic expressions are used in a wide range of real-life situations, including:

  • Science: Algebraic expressions are used to model and solve problems in physics, chemistry, and biology.
  • Engineering: Algebraic expressions are used to design and optimize systems, such as bridges and buildings.
  • Economics: Algebraic expressions are used to model and analyze economic systems and make predictions about future trends.

Common Algebraic Expressions

Q: What is the formula for the area of a circle?

A: The formula for the area of a circle is:

A=Ï€r2A = \pi r^2

Q: What is the formula for the volume of a sphere?

A: The formula for the volume of a sphere is:

V=43Ï€r3V = \frac{4}{3} \pi r^3

Q: What is the formula for the slope of a line?

A: The formula for the slope of a line is:

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

Tips and Tricks

Q: How can I make algebraic expressions easier to understand?

A: To make algebraic expressions easier to understand, try:

  • Using visual aids, such as graphs and charts.
  • Breaking down complex expressions into simpler components.
  • Using real-life examples to illustrate the concepts.

Q: How can I improve my algebraic expression skills?

A: To improve your algebraic expression skills, try:

  • Practicing regularly with exercises and problems.
  • Seeking help from a tutor or teacher.
  • Using online resources and tools to supplement your learning.

Conclusion

Algebraic expressions are a fundamental concept in mathematics, and understanding them is essential for success in math and science. By following the rules of exponents, applying the order of operations, and using visual aids and real-life examples, you can make algebraic expressions easier to understand and improve your skills. Remember to practice regularly and seek help when needed to become proficient in algebraic expressions.

Frequently Asked Questions

Q: What is the difference between an algebraic expression and an equation?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations, while an equation is a statement that two expressions are equal.

Q: How do I solve an algebraic equation?

A: To solve an algebraic equation, you need to isolate the variable by performing inverse operations.

Q: What is the importance of algebraic expressions in computer science?

A: Algebraic expressions are used in computer science to model and solve problems in programming, data analysis, and machine learning.

References