Choose The Correct Simplification Of $\frac{f^9 H^{23}}{f^3 H^{17}}$:A. $f^{12} H^6$ B. $\frac{1}{f^{12} H^6}$ C. $f^6 H^6$ D. $\frac{1}{f^6 H^6}$

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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 correct simplification of the given expression f9h23f3h17\frac{f^9 h^{23}}{f^3 h^{17}}. We will examine each option and determine the correct answer.

Understanding Exponents

Before we dive into the simplification process, it's essential to understand the concept of exponents. Exponents are a shorthand way of representing repeated multiplication. For example, a3a^3 can be written as a×a×aa \times a \times a. When we have a fraction with exponents, we can simplify it by subtracting the exponents of the denominator from the exponents of the numerator.

Simplifying the Expression

Now that we have a solid understanding of exponents, let's simplify the given expression f9h23f3h17\frac{f^9 h^{23}}{f^3 h^{17}}. To do this, we need to subtract the exponents of the denominator from the exponents of the numerator.

f9h23f3h17=f9−3h23−17\frac{f^9 h^{23}}{f^3 h^{17}} = f^{9-3} h^{23-17}

Applying the Rules of Exponents

Now that we have simplified the expression, we can apply the rules of exponents to further simplify it. When we subtract exponents, we can combine the terms with the same base.

f9−3h23−17=f6h6f^{9-3} h^{23-17} = f^6 h^6

Evaluating the Options

Now that we have simplified the expression, let's evaluate the options.

  • Option A: f12h6f^{12} h^6 - This option is incorrect because the exponent of ff is not 1212, but rather 66.
  • Option B: 1f12h6\frac{1}{f^{12} h^6} - This option is incorrect because the exponent of ff is not 1212, but rather 66, and the expression is not in the correct form.
  • Option C: f6h6f^6 h^6 - This option is correct because it matches the simplified expression we obtained earlier.
  • Option D: 1f6h6\frac{1}{f^6 h^6} - This option is incorrect because the expression is not in the correct form.

Conclusion

In conclusion, the correct simplification of the expression f9h23f3h17\frac{f^9 h^{23}}{f^3 h^{17}} is f6h6f^6 h^6. This is achieved by subtracting the exponents of the denominator from the exponents of the numerator and applying the rules of exponents. We evaluated each option and determined that only option C is correct.

Tips and Tricks

  • When simplifying algebraic expressions, it's essential to understand the concept of exponents and how to apply the rules of exponents.
  • When subtracting exponents, combine the terms with the same base.
  • Always evaluate each option carefully to ensure that it matches the simplified expression.

Common Mistakes

  • Failing to understand the concept of exponents and how to apply the rules of exponents.
  • Not combining the terms with the same base when subtracting exponents.
  • Not evaluating each option carefully to ensure that it matches the simplified expression.

Real-World Applications

Simplifying algebraic expressions is a crucial skill in many real-world applications, including:

  • Science and Engineering: Algebraic expressions are used to describe complex systems and relationships in science and engineering.
  • Computer Programming: Algebraic expressions are used to write efficient and effective code in computer programming.
  • Finance: Algebraic expressions are used to calculate interest rates and investment returns in finance.

Introduction

In our previous article, we explored the process of simplifying algebraic expressions, with a focus on the correct simplification of the expression f9h23f3h17\frac{f^9 h^{23}}{f^3 h^{17}}. We also discussed the importance of understanding exponents and applying the rules of exponents to simplify expressions. In this article, we will provide a Q&A guide to help you better understand the concept of simplifying algebraic expressions.

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to understand the concept of exponents and how to apply the rules of exponents. Exponents are a shorthand way of representing repeated multiplication, and the rules of exponents state that when we multiply two numbers with the same base, we add their exponents.

Q: How do I simplify an expression with exponents?

A: To simplify an expression with exponents, we need to subtract the exponents of the denominator from the exponents of the numerator. For example, if we have the expression f9h23f3h17\frac{f^9 h^{23}}{f^3 h^{17}}, we can simplify it by subtracting the exponents of the denominator from the exponents of the numerator.

Q: What is the rule for subtracting exponents?

A: The rule for subtracting exponents is that when we subtract exponents, we can combine the terms with the same base. For example, if we have the expression f9h23÷f3h17f^9 h^{23} \div f^3 h^{17}, we can simplify it by subtracting the exponents of the denominator from the exponents of the numerator.

Q: How do I apply the rules of exponents to simplify an expression?

A: To apply the rules of exponents to simplify an expression, we need to follow these steps:

  1. Understand the concept of exponents and how to apply the rules of exponents.
  2. Simplify the expression by subtracting the exponents of the denominator from the exponents of the numerator.
  3. Combine the terms with the same base.
  4. Evaluate the expression to ensure that it is in the correct form.

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

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

  • Failing to understand the concept of exponents and how to apply the rules of exponents.
  • Not combining the terms with the same base when subtracting exponents.
  • Not evaluating each option carefully to ensure that it matches the simplified expression.

Q: How do I evaluate each option carefully to ensure that it matches the simplified expression?

A: To evaluate each option carefully, you need to follow these steps:

  1. Simplify the expression by subtracting the exponents of the denominator from the exponents of the numerator.
  2. Combine the terms with the same base.
  3. Evaluate each option carefully to ensure that it matches the simplified expression.
  4. Check your work to ensure that you have not made any errors.

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

A: Some real-world applications of simplifying algebraic expressions include:

  • Science and Engineering: Algebraic expressions are used to describe complex systems and relationships in science and engineering.
  • Computer Programming: Algebraic expressions are used to write efficient and effective code in computer programming.
  • Finance: Algebraic expressions are used to calculate interest rates and investment returns in finance.

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill in mathematics, and it has many real-world applications. By understanding the concept of exponents and applying the rules of exponents, you can simplify expressions and make informed decisions in your personal and professional life. Remember to avoid common mistakes and evaluate each option carefully to ensure that it matches the simplified expression.

Tips and Tricks

  • When simplifying algebraic expressions, it's essential to understand the concept of exponents and how to apply the rules of exponents.
  • When subtracting exponents, combine the terms with the same base.
  • Always evaluate each option carefully to ensure that it matches the simplified expression.

Common Mistakes

  • Failing to understand the concept of exponents and how to apply the rules of exponents.
  • Not combining the terms with the same base when subtracting exponents.
  • Not evaluating each option carefully to ensure that it matches the simplified expression.

Real-World Applications

Simplifying algebraic expressions is a crucial skill in many real-world applications, including:

  • Science and Engineering: Algebraic expressions are used to describe complex systems and relationships in science and engineering.
  • Computer Programming: Algebraic expressions are used to write efficient and effective code in computer programming.
  • Finance: Algebraic expressions are used to calculate interest rates and investment returns in finance.

By mastering the skill of simplifying algebraic expressions, you can apply it to a wide range of real-world applications and make informed decisions in your personal and professional life.