Choose The Correct Simplification Of X 12 Z 11 X 2 Z 4 \frac{x^{12} Z^{11}}{x^2 Z^4} X 2 Z 4 X 12 Z 11 ​ .A. X 10 Z 7 X^{10} Z^7 X 10 Z 7 B. X 14 Z 15 X^{14} Z^{15} X 14 Z 15 C. 1 X 10 Z 7 \frac{1}{x^{10} Z^7} X 10 Z 7 1 ​ D. 1 X 14 Z 15 \frac{1}{x^{14} Z^{15}} X 14 Z 15 1 ​

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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 focus on simplifying a specific algebraic expression, x12z11x2z4\frac{x^{12} z^{11}}{x^2 z^4}, and explore the different options available. We will also discuss the importance of simplifying algebraic expressions and provide a step-by-step guide on how to do it.

What is Simplification in Algebra?

Simplification in algebra refers to the process of reducing a complex algebraic expression to its simplest form. This involves combining like terms, canceling out common factors, and rearranging the expression to make it easier to understand and work with. Simplification is an essential skill in algebra, as it helps to:

  • Make expressions easier to read and understand
  • Reduce the complexity of calculations
  • Identify patterns and relationships between variables
  • Solve equations and inequalities more efficiently

The Expression to Simplify

The expression we will be simplifying is x12z11x2z4\frac{x^{12} z^{11}}{x^2 z^4}. This expression involves variables xx and zz, and we need to simplify it by combining like terms and canceling out common factors.

Step 1: Factor Out Common Terms

To simplify the expression, we need to factor out common terms from the numerator and denominator. In this case, we can factor out x2x^2 from the numerator and z4z^4 from the denominator.

import sympy as sp

x, z = sp.symbols('x z')



expr = (x12 * z11) / (x2 * z4)



factored_expr = sp.factor(expr)
print(factored_expr)

Step 2: Cancel Out Common Factors

Once we have factored out common terms, we can cancel out common factors between the numerator and denominator. In this case, we can cancel out x2x^2 and z4z^4.

# Cancel out common factors
canceled_expr = sp.cancel(factored_expr)
print(canceled_expr)

Step 3: Simplify the Expression

After canceling out common factors, we can simplify the expression by combining like terms. In this case, we can combine the remaining terms to get the simplified expression.

# Simplify the expression
simplified_expr = sp.simplify(canceled_expr)
print(simplified_expr)

The Final Answer

After simplifying the expression, we get:

x10z7x^{10} z^7

This is the correct simplification of the given expression.

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics, and it requires a step-by-step approach. By factoring out common terms, canceling out common factors, and simplifying the expression, we can reduce complex expressions to their simplest form. In this article, we have simplified the expression x12z11x2z4\frac{x^{12} z^{11}}{x^2 z^4} and identified the correct answer as x10z7x^{10} z^7. We hope this article has provided a clear understanding of the simplification process and has helped you to develop your algebraic skills.

Discussion

What do you think is the most challenging part of simplifying algebraic expressions? Do you have any tips or tricks for simplifying complex expressions? Share your thoughts and experiences in the comments below!

References

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Q: What is the purpose of simplifying algebraic expressions?

A: The purpose of simplifying algebraic expressions is to reduce complex expressions to their simplest form, making it easier to understand and work with. Simplification helps to:

  • Make expressions easier to read and understand
  • Reduce the complexity of calculations
  • Identify patterns and relationships between variables
  • Solve equations and inequalities more efficiently

Q: What are the steps involved in simplifying algebraic expressions?

A: The steps involved in simplifying algebraic expressions are:

  1. Factor out common terms from the numerator and denominator
  2. Cancel out common factors between the numerator and denominator
  3. Simplify the expression by combining like terms

Q: How do I factor out common terms from the numerator and denominator?

A: To factor out common terms from the numerator and denominator, you can use the following steps:

  1. Identify the common terms in the numerator and denominator
  2. Factor out the common terms from the numerator and denominator
  3. Write the factored expression in the form of a product of the common terms and the remaining terms

Q: How do I cancel out common factors between the numerator and denominator?

A: To cancel out common factors between the numerator and denominator, you can use the following steps:

  1. Identify the common factors between the numerator and denominator
  2. Cancel out the common factors by dividing the numerator and denominator by the common factor
  3. Write the canceled expression in the form of a product of the remaining terms

Q: What is the difference between simplifying and solving algebraic expressions?

A: Simplifying and solving algebraic expressions are two different processes:

  • Simplifying involves reducing complex expressions to their simplest form
  • Solving involves finding the value of the expression that satisfies a given equation or inequality

Q: Can I use a calculator to simplify algebraic expressions?

A: Yes, you can use a calculator to simplify algebraic expressions. However, it's essential to understand the underlying math concepts and be able to simplify expressions manually.

Q: Are there any online tools or resources that can help me simplify algebraic expressions?

A: Yes, there are several online tools and resources that can help you simplify algebraic expressions, including:

  • Sympy library
  • Wolfram Alpha
  • Mathway

Q: Can I simplify algebraic expressions with variables and constants?

A: Yes, you can simplify algebraic expressions with variables and constants. The process involves factoring out common terms, canceling out common factors, and simplifying the expression.

Q: Are there any tips or tricks for simplifying algebraic expressions?

A: Yes, here are some tips and tricks for simplifying algebraic expressions:

  • Use the distributive property to simplify expressions
  • Factor out common terms from the numerator and denominator
  • Cancel out common factors between the numerator and denominator
  • Simplify the expression by combining like terms

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics, and it requires a step-by-step approach. By understanding the purpose of simplification, following the steps involved, and using online tools and resources, you can simplify complex expressions and develop your algebraic skills. Remember to practice regularly and seek help when needed to become proficient in simplifying algebraic expressions.

Discussion

What do you think is the most challenging part of simplifying algebraic expressions? Do you have any tips or tricks for simplifying complex expressions? Share your thoughts and experiences in the comments below!

References

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