Evaluate. ( − 6 ) 2 (-6)^2 ( − 6 ) 2 ( − 6 ) 2 = □ (-6)^2 = \square ( − 6 ) 2 = □ (Simplify Your Answer.)

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Understanding the Problem

When evaluating the expression (6)2(-6)^2, we need to simplify it to find the final answer. The expression involves a negative number raised to the power of 2, which can be a bit tricky to handle. In this discussion, we will explore the rules of exponents and how to simplify expressions involving negative numbers.

Rules of Exponents

To simplify the expression (6)2(-6)^2, we need to understand the rules of exponents. The exponent 2 indicates that we need to multiply the base number -6 by itself 2 times. This can be written as:

(6)2=(6)×(6)(-6)^2 = (-6) \times (-6)

Multiplying Negative Numbers

When multiplying two negative numbers, we need to remember that the product of two negative numbers is always positive. This is a fundamental rule in mathematics that can be applied to any situation involving the multiplication of negative numbers.

Simplifying the Expression

Now that we have understood the rules of exponents and the multiplication of negative numbers, we can simplify the expression (6)2(-6)^2. We will multiply the base number -6 by itself 2 times:

(6)2=(6)×(6)=36(-6)^2 = (-6) \times (-6) = 36

Conclusion

In this discussion, we have evaluated the expression (6)2(-6)^2 and simplified it to find the final answer. We have applied the rules of exponents and the multiplication of negative numbers to arrive at the solution. The final answer is 36.

Frequently Asked Questions

  • What is the rule for multiplying negative numbers? When multiplying two negative numbers, the product is always positive.
  • How do we simplify expressions involving negative numbers? We apply the rules of exponents and the multiplication of negative numbers to simplify the expression.
  • What is the final answer to the expression (6)2(-6)^2? The final answer is 36.

Additional Resources

  • Rules of Exponents: A comprehensive guide to the rules of exponents, including the multiplication of negative numbers.
  • Negative Numbers: A discussion on the properties and rules of negative numbers, including the multiplication of negative numbers.
  • Exponents: A tutorial on the rules of exponents, including the multiplication of negative numbers.

Final Answer

The final answer to the expression (6)2(-6)^2 is 36.

Understanding the Basics

Evaluating expressions with negative numbers can be a bit tricky, but with the right rules and techniques, you can simplify even the most complex expressions. In this Q&A article, we will cover some common questions and answers related to evaluating expressions with negative numbers.

Q: What is the rule for multiplying negative numbers?

A: When multiplying two negative numbers, the product is always positive. This is a fundamental rule in mathematics that can be applied to any situation involving the multiplication of negative numbers.

Q: How do I simplify expressions involving negative numbers?

A: To simplify expressions involving negative numbers, you need to apply the rules of exponents and the multiplication of negative numbers. For example, if you have an expression like (6)2(-6)^2, you would multiply the base number -6 by itself 2 times.

Q: What is the difference between (6)2(-6)^2 and 626^2?

A: The expression (6)2(-6)^2 involves a negative number raised to the power of 2, while the expression 626^2 involves a positive number raised to the power of 2. When evaluating (6)2(-6)^2, you would multiply the base number -6 by itself 2 times, resulting in a positive answer. On the other hand, when evaluating 626^2, you would multiply the base number 6 by itself 2 times, resulting in a positive answer.

Q: Can I simplify expressions involving negative numbers using a calculator?

A: Yes, you can simplify expressions involving negative numbers using a calculator. However, it's always a good idea to understand the underlying rules and techniques before relying on a calculator. This will help you to avoid making mistakes and to develop a deeper understanding of the mathematics involved.

Q: How do I handle expressions with multiple negative numbers?

A: When handling expressions with multiple negative numbers, you need to apply the rules of exponents and the multiplication of negative numbers. For example, if you have an expression like (6)×(3)×(2)(-6) \times (-3) \times (-2), you would multiply the base numbers together, taking into account the signs of each number.

Q: What is the final answer to the expression (6)2(-6)^2?

A: The final answer to the expression (6)2(-6)^2 is 36.

Q: Can I use the order of operations to simplify expressions involving negative numbers?

A: Yes, you can use the order of operations to simplify expressions involving negative numbers. The order of operations is a set of rules that dictate the order in which you should perform mathematical operations. By following the order of operations, you can simplify even the most complex expressions.

Q: How do I handle expressions with negative numbers and fractions?

A: When handling expressions with negative numbers and fractions, you need to apply the rules of exponents and the multiplication of negative numbers. For example, if you have an expression like (6)×12(-6) \times \frac{1}{2}, you would multiply the base number -6 by the fraction 12\frac{1}{2}.

Q: What is the final answer to the expression (6)×12(-6) \times \frac{1}{2}?

A: The final answer to the expression (6)×12(-6) \times \frac{1}{2} is -3.

Q: Can I use a calculator to simplify expressions involving negative numbers and fractions?

A: Yes, you can use a calculator to simplify expressions involving negative numbers and fractions. However, it's always a good idea to understand the underlying rules and techniques before relying on a calculator. This will help you to avoid making mistakes and to develop a deeper understanding of the mathematics involved.

Q: How do I handle expressions with negative numbers and decimals?

A: When handling expressions with negative numbers and decimals, you need to apply the rules of exponents and the multiplication of negative numbers. For example, if you have an expression like (6.5)×(2.5)(-6.5) \times (-2.5), you would multiply the base numbers together, taking into account the signs of each number.

Q: What is the final answer to the expression (6.5)×(2.5)(-6.5) \times (-2.5)?

A: The final answer to the expression (6.5)×(2.5)(-6.5) \times (-2.5) is 16.25.

Q: Can I use a calculator to simplify expressions involving negative numbers and decimals?

A: Yes, you can use a calculator to simplify expressions involving negative numbers and decimals. However, it's always a good idea to understand the underlying rules and techniques before relying on a calculator. This will help you to avoid making mistakes and to develop a deeper understanding of the mathematics involved.

Final Answer

The final answer to the expression (6)2(-6)^2 is 36.