Simplify The Expression:B) $\frac{5a^2b \times 3(ab)^2}{5ab}$

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying the expression $\frac{5a^2b \times 3(ab)^2}{5ab}$, which involves various algebraic manipulations. We will break down the expression into smaller parts, apply the rules of exponents, and simplify the resulting expression.

Understanding the Expression

The given expression is $\frac{5a^2b \times 3(ab)^2}{5ab}$. To simplify this expression, we need to understand the rules of exponents and how to manipulate them. The expression involves multiplication and division of variables with exponents.

Applying the Rules of Exponents

The first step in simplifying the expression is to apply the rules of exponents. The expression $\frac{5a^2b \times 3(ab)^2}{5ab}$ can be rewritten as $\frac{5a^2b \times 3a^2b^2}{5ab}$. We can simplify this expression by combining like terms and applying the rules of exponents.

Simplifying the Expression

To simplify the expression, we need to apply the following rules:

• When multiplying variables with the same base, we add the exponents.
• When dividing variables with the same base, we subtract the exponents.
• When multiplying or dividing variables with different bases, we multiply or divide the coefficients and keep the variables separate.

Using these rules, we can simplify the expression as follows:

$\frac{5a^2b \times 3a^2b^2}{5ab} = \frac{15a^4b^3}{5ab}$

Further Simplification

We can further simplify the expression by dividing the coefficients and subtracting the exponents:

$\frac{15a^4b^3}{5ab} = 3a^3b^2$

Conclusion

In this article, we simplified the expression $\frac{5a^2b \times 3(ab)^2}{5ab}$ by applying the rules of exponents and combining like terms. We broke down the expression into smaller parts, manipulated the variables with exponents, and simplified the resulting expression. The final simplified expression is $3a^3b^2$.

Tips and Tricks

• When simplifying algebraic expressions, it's essential to understand the rules of exponents and how to manipulate them.
• Always combine like terms and apply the rules of exponents to simplify the expression.
• When dividing variables with the same base, subtract the exponents.
• When multiplying or dividing variables with different bases, multiply or divide the coefficients and keep the variables separate.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications in various fields, including:

• Physics: Algebraic expressions are used to describe the motion of objects and the behavior of physical systems.
• Engineering: Algebraic expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Algebraic expressions are used to model economic systems and make predictions about economic trends.

Final Thoughts

Simplifying algebraic expressions is a crucial skill for students and professionals alike. By understanding the rules of exponents and how to manipulate them, we can simplify complex expressions and make them more manageable. In this article, we simplified the expression $\frac{5a^2b \times 3(ab)^2}{5ab}$ by applying the rules of exponents and combining like terms. We hope that this article has provided valuable insights and tips for simplifying algebraic expressions.

Introduction

In our previous article, we simplified the expression $\frac{5a^2b \times 3(ab)^2}{5ab}$ by applying the rules of exponents and combining like terms. In this article, we will provide a Q&A section to address common questions and concerns related to simplifying algebraic expressions.

Q&A

Q: What are the rules of exponents?

A: The rules of exponents are a set of rules that govern how to manipulate variables with exponents. The main rules are:

• When multiplying variables with the same base, we add the exponents.
• When dividing variables with the same base, we subtract the exponents.
• When multiplying or dividing variables with different bases, we multiply or divide the coefficients and keep the variables separate.

Q: How do I simplify an algebraic expression?

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

1. Identify the variables and their exponents.
2. Apply the rules of exponents to combine like terms.
3. Simplify the resulting expression by dividing the coefficients and subtracting the exponents.

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

A: A coefficient is a number that is multiplied by a variable, while a variable is a letter or symbol that represents a value. For example, in the expression $3x$, the coefficient is 3 and the variable is x.

Q: How do I handle negative exponents?

A: When a variable has a negative exponent, we can rewrite it as a fraction with the variable in the numerator and the reciprocal of the exponent in the denominator. For example, $x^{-2}$ can be rewritten as $\frac{1}{x^2}$.

Q: Can I simplify an expression with multiple variables?

A: Yes, you can simplify an expression with multiple variables by applying the rules of exponents and combining like terms. For example, $\frac{2x^2y \times 3x^2y^2}{2xy}$ can be simplified as $3x^3y$.

Q: What is the order of operations when simplifying an expression?

A: The order of operations when simplifying an expression is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate expressions with exponents next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate addition and subtraction operations from left to right.

Tips and Tricks

• Always follow the order of operations when simplifying an expression.
• Identify the variables and their exponents before applying the rules of exponents.
• Simplify the resulting expression by dividing the coefficients and subtracting the exponents.
• Use fractions to handle negative exponents.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications in various fields, including:

• Physics: Algebraic expressions are used to describe the motion of objects and the behavior of physical systems.
• Engineering: Algebraic expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Algebraic expressions are used to model economic systems and make predictions about economic trends.

Final Thoughts

Simplifying algebraic expressions is a crucial skill for students and professionals alike. By understanding the rules of exponents and how to manipulate them, we can simplify complex expressions and make them more manageable. In this article, we provided a Q&A section to address common questions and concerns related to simplifying algebraic expressions. We hope that this article has provided valuable insights and tips for simplifying algebraic expressions.