17. Copy And Complete The Table.$\[ \begin{tabular}{|l|c|c|} \hline \multicolumn{1}{|c|}{\text{Expression}} & \begin{tabular}{c} \text{Repeated} \\ \text{Multiplication} \end{tabular} & \text{Powers} \\ \hline a) $[2 \times (-5)]^3$ & &

Feb 28, 2025 by ADMIN 242 views

Understanding the Table: A Guide to Repeated Multiplication and Powers

In mathematics, there are various ways to represent and solve expressions. One of the fundamental concepts is repeated multiplication, which is a crucial aspect of algebra and arithmetic. In this article, we will delve into the world of repeated multiplication and powers, exploring how they are used to simplify and solve mathematical expressions.

What is Repeated Multiplication?

Repeated multiplication is a mathematical operation where a number is multiplied by itself multiple times. This operation is denoted by the exponentiation symbol (^) or the multiplication symbol (×) repeated multiple times. For example, 2 × 2 × 2 can be written as 2^3, where 2 is the base and 3 is the exponent.

What are Powers?

Powers, also known as exponents, are a shorthand way of representing repeated multiplication. In the previous example, 2^3 means 2 multiplied by itself 3 times. Powers are used to simplify complex expressions and make them easier to work with.

The Table: A Closer Look

The table provided is a comparison of two different methods of representing mathematical expressions: repeated multiplication and powers. The table has three columns: Expression, Repeated Multiplication, and Powers.

Expression	Repeated Multiplication	Powers
a) [2 × (-5)]^3

Completing the Table

To complete the table, we need to fill in the Repeated Multiplication and Powers columns for each expression. Let's start with the first expression: [2 × (-5)]^3.

Repeated Multiplication

To find the repeated multiplication of [2 × (-5)]^3, we need to multiply 2 by (-5) three times.

2 × (-5) = -10 -10 × (-5) = 50 50 × (-5) = -250

So, the repeated multiplication of [2 × (-5)]^3 is -250.

Powers

To find the powers of [2 × (-5)]^3, we need to raise the result of 2 × (-5) to the power of 3.

2 × (-5) = -10 (-10)^3 = -1000

So, the powers of [2 × (-5)]^3 is -1000.

Conclusion

In conclusion, the table provides a comparison of two different methods of representing mathematical expressions: repeated multiplication and powers. By understanding the concept of repeated multiplication and powers, we can simplify complex expressions and make them easier to work with. The completed table shows that the repeated multiplication and powers of [2 × (-5)]^3 are -250 and -1000, respectively.

Frequently Asked Questions

What is repeated multiplication? Repeated multiplication is a mathematical operation where a number is multiplied by itself multiple times.
What are powers? Powers, also known as exponents, are a shorthand way of representing repeated multiplication.
How do I complete the table? To complete the table, you need to fill in the Repeated Multiplication and Powers columns for each expression.

Further Reading

Algebra: A Comprehensive Guide
Arithmetic: A Beginner's Guide
Exponents: A Detailed Explanation

References

[1] Khan Academy. (n.d.). Exponents. Retrieved from https://www.khanacademy.org/math/algebra/x2f-exponents
[2] Math Is Fun. (n.d.). Exponents. Retrieved from https://www.mathisfun.com/algebra/exponents.html

Table of Contents

Understanding the Table: A Guide to Repeated Multiplication and Powers
What is Repeated Multiplication?
What are Powers?
The Table: A Closer Look
Completing the Table
Repeated Multiplication
Powers
Conclusion
Frequently Asked Questions
Further Reading
References
Table of Contents
Q&A: Repeated Multiplication and Powers

In our previous article, we explored the concept of repeated multiplication and powers, and how they are used to simplify and solve mathematical expressions. In this article, we will answer some of the most frequently asked questions about repeated multiplication and powers.

Q: What is repeated multiplication?

A: Repeated multiplication is a mathematical operation where a number is multiplied by itself multiple times. This operation is denoted by the exponentiation symbol (^) or the multiplication symbol (×) repeated multiple times.

Q: What are powers?

A: Powers, also known as exponents, are a shorthand way of representing repeated multiplication. In the previous example, 2^3 means 2 multiplied by itself 3 times.

Q: How do I calculate repeated multiplication?

A: To calculate repeated multiplication, you need to multiply the base number by itself as many times as indicated by the exponent. For example, 2^3 means 2 multiplied by itself 3 times: 2 × 2 × 2 = 8.

Q: What is the difference between repeated multiplication and powers?

A: Repeated multiplication and powers are two different ways of representing the same operation. Repeated multiplication is a more explicit way of showing the multiplication, while powers are a shorthand way of representing the same operation.

Q: Can I use powers with negative numbers?

A: Yes, you can use powers with negative numbers. For example, (-2)^3 means -2 multiplied by itself 3 times: (-2) × (-2) × (-2) = -8.

Q: Can I use powers with fractions?

A: Yes, you can use powers with fractions. For example, (1/2)^3 means 1/2 multiplied by itself 3 times: (1/2) × (1/2) × (1/2) = 1/8.

Q: How do I simplify expressions with powers?

A: To simplify expressions with powers, you need to follow the order of operations (PEMDAS):

Evaluate any expressions inside parentheses.
Evaluate any exponents (powers).
Multiply and divide from left to right.
Add and subtract from left to right.

Q: Can I use powers with variables?

A: Yes, you can use powers with variables. For example, x^2 means x multiplied by itself 2 times: x × x = x^2.

Q: How do I calculate the value of a power with a variable?

A: To calculate the value of a power with a variable, you need to substitute the value of the variable into the expression. For example, if x = 3, then x^2 = 3^2 = 9.

Q: Can I use powers with decimals?

A: Yes, you can use powers with decimals. For example, (0.5)^3 means 0.5 multiplied by itself 3 times: (0.5) × (0.5) × (0.5) = 0.125.

Q: How do I simplify expressions with powers and decimals?

A: To simplify expressions with powers and decimals, you need to follow the order of operations (PEMDAS):

Evaluate any expressions inside parentheses.
Evaluate any exponents (powers).
Multiply and divide from left to right.
Add and subtract from left to right.