Exponents

1. What is an Exponent?

Imagine your teacher asks you to write this on the whiteboard:

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Your hand will feel very tired, right?

In math, we have a shortcut to write long multiplications. We write it like this:

2¹⁰

🔹The Big Number (2) is called the Base. This is the number that multiplies itself.

🔹The Small Number (10) is called the Exponent or Power. It tells you how many times you repeat the multiplication.

So, 2¹⁰ simply means: “Multiply 2 by itself, 10 times!”

2. The Golden Rules of Exponents

To solve exponent problems easily, you only need to remember these simple rules:

Rule A: Multiplication (Add the Powers)

If the base numbers are the same and you multiply them, just add the exponents.

Formula:

Example:

Rule B: Division (Subtract the Powers)

If the base numbers are the same and you divide them, just subtract the exponents.

Formula:

Example:

Rule C: Power of a Power (Multiply the Powers)

If a power is inside a bracket, and there is another power outside, just multiply them together.

Formula: (aᵐ)ⁿ ﹦ aᵐ×ⁿ                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           

Example: (5²)³ = 5⁶

Rule D: The Zero Power (Always Equals 1)

Any number (except zero) with a power of 0 is always equal to 1. It does not matter how big the number is!

Formula: a⁰ = 1

Example: 100⁰ = 1

Let’s Try One Example!

Let’s simplify this problem step-by-step:

Step 2: Do the Division.
Subtract the powers: (7 – 5 = 2). So, it becomes 2².

Step 1: Do the top part first (Multiplication).
Add the powers: (3 + 4 = 7). So, it becomes 2⁷.

Step 3: Calculate the final answer.
2² = 2 x 2 = 4.

The final answer is 4. Super easy, right?