Math Notes: Indices!

Section 1: Index Notation

🌟 Introduction

In mathematics, there are instances when a number has to be multiplied repeatedly and written. For example, we can write 16 = 2 × 2 × 2 × 2. There is a method of writing a number which is multiplied repeatedly in a concise way.

📚 Theory

When a number is multiplied repeatedly and written in a concise way, we say it is written using indices or in index form.

In the expression 2³, 2 is defined as the base and 3 is defined as the index.
This is read as "two to the power three" or "two to the power of three".
A number to the power two is also called the square of the number (e.g., 5² is five squared).
A number to the power three is also called the cube of the number (e.g., 8³ is eight cubed).
The value of 2³ is equal to the value of 2 × 2 × 2, which is 8.

💡 Examples

Let's look at some examples!

Writing in index notation: 3 × 3 × 3 × 3 = 3⁴.
Finding the value: 2⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64.
Mixing numbers: 2 × 2 × 2 × 5 × 5 = 2³ × 5².
Value of a mixed product: 5² × 7³ = 5 × 5 × 7 × 7 × 7 = 8575.

🧠 Quiz Time: Section 1

Select the right answer! Correct answers turn blue, wrong answers turn red.

1. In the number 2³, what is the 2 called?

2. In the number 2³, what is the 3 called?

3. How can you write 2 × 2 × 2 in index form?

4. What is another way to say "five to the power two"?

5. What is another way to say "eight to the power three"?

6. Write 3 × 3 × 3 × 3 using index notation.

7. What is the value of 2³?

8. What is the value of 7²?

9. Write 10 × 10 × 10 in index form.

10. What is the value of 2⁶?

Section 2: Representing a Number as a Power

🌟 Introduction

Sometimes we have a big number and want to shrink it into index form! To express a number like 16 as a power of 2, it is necessary to know how many times 2 should be multiplied by itself to obtain the value 16.

📚 Theory

It is easy to use division to find the number of times a particular number should be multiplied to obtain a given number.

When the base is identified, to find the index, the main number should be divided repeatedly by the base.
Division is used to find the index when expressing a number as a power of another number.

💡 Examples

Let's practice turning numbers into powers!

16 as a power of 2: Divide 16 repeatedly by 2 to get 2 × 2 × 2 × 2, which equals 2⁴.
81 as a power of 3: Divide 81 repeatedly by 3 to get 3 × 3 × 3 × 3, which equals 3⁴.
125 as a power of 5: Divide 125 repeatedly by 5 to get 5 × 5 × 5, which equals 5³.

🧠 Quiz Time: Section 2

Select the right answer! Correct answers turn blue, wrong answers turn red.

11. Write 16 as a power of 2.

12. Write 81 as a power of 3.

13. Write 125 as a power of 5.

14. Write 32 as a power of 2.

15. What mathematical operation is used to find the index when expressing a number as a power?

16. True or False: 3² = 6

17. True or False: 2³ = 8

18. Write 64 as a power of 8.

19. Write 144 as a power of 12.

20. True or False: 5³ = 15

Super Math Notes: All About Indices! 🚀

Section 1: Index Notation

🌟 Introduction

📚 Theory

💡 Examples

🧠 Quiz Time: Section 1

Section 2: Representing a Number as a Power

🌟 Introduction

📚 Theory

💡 Examples

🧠 Quiz Time: Section 2