Simplify The Expression Completely: ${\frac{13x {19}}{23x 6}}$Answer =

Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will focus on simplifying the given expression ${\frac{13x^{19}}{23x6}}$. We will break down the steps involved in simplifying this expression and provide a clear explanation of the process.

Understanding the Expression

The given expression is a fraction with a numerator of $13x^{19}$ and a denominator of $23x^6$. To simplify this expression, we need to apply the rules of exponents and fractions.

Simplifying the Expression

To simplify the expression, we can start by dividing the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of $13x^{19}$ and $23x^6$ is $x^6$. We can divide both the numerator and denominator by $x^6$ to simplify the expression.

import sympy as sp
x = sp.symbols('x')

expr = (13x**19) / (23x**6)

simplified_expr = sp.simplify(expr)
print(simplified_expr)

Applying the Quotient Rule

When simplifying the expression, we can also apply the quotient rule of exponents. The quotient rule states that when dividing two powers with the same base, we subtract the exponents.

import sympy as sp

x = sp.symbols('x')

expr = (13x**19) / (23x**6)

simplified_expr = (13/23) * (x**(19-6))
print(simplified_expr)

Simplifying the Fraction

Now that we have applied the quotient rule, we can simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of $13$ and $23$ is $1$, so we cannot simplify the fraction further.

Final Answer

The final simplified expression is ${\frac{13}{23}x^{13}}$.

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we have broken down the steps involved in simplifying the given expression ${\frac{13x^{19}}{23x6}}$. We have applied the rules of exponents and fractions, and used the quotient rule to simplify the expression. The final simplified expression is ${\frac{13}{23}x^{13}}$.

Frequently Asked Questions

• What is the greatest common factor (GCF) of $13x^{19}$ and $23x^6$?
• How do we apply the quotient rule of exponents?
• What is the final simplified expression?

Answers

• The greatest common factor (GCF) of $13x^{19}$ and $23x^6$ is $x^6$.
• To apply the quotient rule of exponents, we subtract the exponents when dividing two powers with the same base.
• The final simplified expression is ${\frac{13}{23}x^{13}}$.

Further Reading

• Simplifying Algebraic Expressions: A Comprehensive Guide
• The Quotient Rule of Exponents: A Detailed Explanation
• Simplifying Fractions: A Step-by-Step Guide
  

Introduction

In our previous article, we simplified the expression ${\frac{13x^{19}}{23x6}}$ using the rules of exponents and fractions. We applied the quotient rule to simplify the expression and arrived at the final simplified expression ${\frac{13}{23}x^{13}}$. In this article, we will answer some frequently asked questions related to simplifying algebraic expressions.

Q&A

Q1: What is the greatest common factor (GCF) of $13x^{19}$ and $23x^6$?

A1: The greatest common factor (GCF) of $13x^{19}$ and $23x^6$ is $x^6$.

Q2: How do we apply the quotient rule of exponents?

A2: To apply the quotient rule of exponents, we subtract the exponents when dividing two powers with the same base. In this case, we subtracted the exponent of $x^6$ from the exponent of $x^{19}$ to get $x^{13}$.

Q3: What is the final simplified expression?

A3: The final simplified expression is ${\frac{13}{23}x^{13}}$.

Q4: Can we simplify the fraction further?

A4: No, we cannot simplify the fraction further because the greatest common factor (GCF) of $13$ and $23$ is $1$.

Q5: What is the significance of simplifying algebraic expressions?

A5: Simplifying algebraic expressions is crucial in mathematics because it helps us to:

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

Q6: How do we know when to apply the quotient rule of exponents?

A6: We apply the quotient rule of exponents when dividing two powers with the same base. In this case, we divided $13x^{19}$ by $23x^6$, and the quotient rule helped us to simplify the expression.

Q7: Can we simplify expressions with negative exponents?

A7: Yes, we can simplify expressions with negative exponents by applying the quotient rule and the rule for negative exponents. For example, if we have the expression ${\frac{2x^{-3}}{3x2}}$, we can simplify it by applying the quotient rule and the rule for negative exponents.

Q8: What is the rule for negative exponents?

A8: The rule for negative exponents states that $a^{-n} = \frac{1}{a^n}$. This means that a negative exponent can be rewritten as a fraction with a positive exponent in the denominator.

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we have answered some frequently asked questions related to simplifying algebraic expressions. We have discussed the greatest common factor (GCF), the quotient rule of exponents, and the rule for negative exponents. We hope that this article has provided you with a better understanding of simplifying algebraic expressions.

Further Reading

• Simplifying Algebraic Expressions: A Comprehensive Guide
• The Quotient Rule of Exponents: A Detailed Explanation
• Simplifying Fractions: A Step-by-Step Guide
• Negative Exponents: A Guide to Understanding and Simplifying