Lesson 1: Exponents (Indices) – Laws and Applications

📝 Introduction

Exponents are everywhere — in science, technology, banking, and even games!
In this lesson, we’ll explore what exponents are, how they work, and the powerful rules (called “laws of indices”) that help us simplify them.
By the end of this lesson, you’ll be able to evaluate, compare, and manipulate exponential expressions with confidence!

🧠 Key Concepts and Explanations

🔢 What is an Exponent?

An exponent (or index) tells us how many times to multiply a number by itself.

Example:

📐 Terminology

In :

• a is the base (number being multiplied)
• n is the exponent or power (number of times to multiply)

📏 Laws of Exponents (Laws of Indices)

These rules help us simplify exponential expressions:

Law	Rule	Example
Product Rule
Quotient Rule
Power of a Power
Zero Exponent
Negative Exponent

🔍 Sample Problem Walkthroughs

✅ Example 1: Using the Product Rule

Question: Simplify

Solution: Add exponents:

✅ Example 2: Negative Exponent

Question: Simplify

Solution:

✅ Example 3: Power of a Power

Question: Simplify

Solution: Multiply the exponents:

📊 Practice Exercises

Part A – Simplify

Part B – True or False?

📝 Answers and Explanations

Part A:

Part B:

1. True
2. True
3. False –
4. False –

🔁 Recap

In this lesson, you learned how exponents work, including how to multiply, divide, and raise powers to other powers.
You also explored the five important laws of indices and applied them in calculations and worded expressions.

💭 Reflection Prompt

Which law of exponents do you find easiest?
Which one is most confusing?
Write your own exponent problem using one of the laws and try solving it — or ask a friend to!