# Indices

## Overview

Welcome to the course material on Indices in General Mathematics. Indices, also known as powers or exponents, play a crucial role in simplifying and manipulating mathematical expressions involving repeated multiplication or division. Understanding the basic concept of indices is fundamental to various mathematical operations involving numbers.

Applying the laws of indices allows us to perform calculations more efficiently and accurately. By following specific rules, we can simplify complex expressions and solve problems with ease. For example, when multiplying two numbers with the same base, the exponents can be added together. This simplification technique is particularly useful when dealing with large numbers or when expressing calculations in a more compact form. Moreover, the laws of indices extend to negative and fractional exponents, further expanding the scope of mathematical operations we can perform.

One essential aspect of working with indices is the ability to express both large and small numbers in standard form. This notation, also known as scientific notation, is a concise and practical way of representing numbers by using powers of 10. By converting numbers into standard form, we can easily compare magnitudes, perform calculations, and communicate numerical information effectively.

Furthermore, the operations involving negative and fractional indices introduce additional challenges and opportunities for learning. Understanding how to manipulate expressions with negative exponents and fractional powers enhances our problem-solving skills and mathematical fluency. The rules governing these operations can be applied across various mathematical contexts, providing a solid foundation for more advanced topics in algebra and calculus.

Tables of squares, square roots, and reciprocals serve as valuable resources in calculations involving indices. These tables provide quick reference points for common calculations, enabling us to streamline our work and minimize errors. By utilizing these tables effectively, we can expedite the process of solving problems and increase our confidence in handling mathematical expressions.

Throughout this course material, we will explore the intricacies of indices, delve into the laws governing their manipulation, practice converting numbers into standard form, and reinforce our understanding through practical examples. By mastering the concepts and techniques related to indices, we can enhance our mathematical proficiency and approach complex problems with confidence.

## Objectives

1. Understand the basic concept of indices
2. Utilize tables of squares, square roots, and reciprocals effectively in calculations
3. Perform operations involving negative and fractional indices
4. Express large and small numbers in standard form
5. Apply the laws of indices in mathematical expressions

## Lesson Note

Indices, also known as exponents or powers, are a way of expressing a number that is being multiplied by itself several times. For example, in the expression $$2^3$$, the number 2 is being multiplied by itself three times: $2^3 = 2 \times 2 \times 2 = 8$ The number 2 is called the base, and the number 3 is called the exponent or index.

## Lesson Evaluation

Congratulations on completing the lesson on Indices. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

1. Simplify the following expression: 2^3 * 2^4. A. 6 B. 16 C. 70 D. 128 Answer: B. 16
2. Evaluate the expression: (5^2)^3 / 5^4. A. 25 B. 5 C. 125 D. 625 Answer: C. 125
3. Solve for x: 3^(x-1) = 27. A. 3 B. 5 C. 4 D. 6 Answer: C. 4
4. Compute the value of: (2^-3) / (2^4). A. 0.015625 B. 16 C. 0.0625 D. 64 Answer: A. 0.015625
5. What is the simplified form of (3^2 * 3^(-1)) / 3^4? A. 1/81 B. 1/243 C. 1/9 D. 27 Answer: C. 1/9
6. If 2^a = 16, what is the value of 'a'? A. 2 B. 3 C. 4 D. 5 Answer: C. 4
7. Determine the value of 5^(1/2) + 5^(-1). A. 1/10 B. 5/2 C. 10 D. 11 Answer: D. 11
8. Simplify (4^-2) / (4^(-3)). A. 4 B. 16 C. 1/4 D. 1/16 Answer: B. 16
9. What is the result of (7^2 * 7^3) / (7^5)? A. 49 B. 7 C. 7^3 D. 7^2 Answer: B. 7

## Past Questions

Wondering what past questions for this topic looks like? Here are a number of questions about Indices from previous years

Question 1

The sum of the interior angles of a regular polygon with k sides is (3k-10) right angles. Find the size of the exterior angle?

Question 1

The difference between an exterior angle of (n - 1) sided regular polygon and an exterior angle of (n + 2) sided regular polygon is 6o, then the value of "n" is

Question 1

Evaluate (25 × 4-2) ÷ (2-3 × 26)

Practice a number of Indices past questions