# Introduction to index notation

^{3} = 4 ´ 4 ´ 4 = 64. The 3 above the 4 tells us to multiply three 4s.

Similarly, 5^{2} = 5 ´ 5 = 25. The 2 tells us to multiply two 5s.

This short-hand way of writing a number that is multiplied several times is called **index notation. **The special terms associated with index notation are demonstrated below.

**Example 1**What is the base and the index of the number 6

^{4}?

Base = 6

Index = 4

**Example 2**

Write 10 ´ 10 ´ 10 ´ 10 ´ 10 in index notation

10 ´ 10 ´ 10 ´ 10 ´ 10 = 10^{5} (we are multiplying five 10s.)

**Example 3**

Write 3^{6} in expanded form.

3^{6} = 3 ´ 3 ´ 3 ´ 3 ´ 3 ´ 3 (six 3s)

**Example 4**

Write 5 ´ 5 ´ 5 ´ 5 ´ 3 ´ 3 ´ 3 in index notation.

5 ´ 5 ´ 5 ´ 5 ´ 3 ´ 3 ´ 3 = 5^{4} ´ 3^{3}

In the Pop Quiz questions, 3^6 means^{ }3^{6}. "^" means "to the power of".