CHAPTER 5

INDICES

INDEX NOTATION1. When a number is multiplied repeatedly by times, it can

be written in index notation

2. Where is the base is the index

times3. Write as repeated multiplication

4096

4. Express in index notation =

𝒂𝒏

Express numbers in index notation Express the number 343 in index notation

using the base 7 Step 1: divide 343 repeatedly by the base 7

until the quotient = 1 Step 2: determine the value of n (number of

times 343 id divided by 7)

3437

497

77

1

Multiplication involving index notation Multiplication Law of Indices

Example 1: simplify = = Example 2: simplify = = =

𝑎𝑚×𝑎𝑛=𝑎𝑚+𝑛

Group the common bases and then simplify them

Example 1: simplify = = = cannot be simplified further

Example 2: simplify

Multiplication involving index notation with different bases

Division involving index notation Division Law of Indices

Example 1: simplify = = Example 2: simplify =

𝑎𝑚÷𝑎𝑛=𝑎𝑚−𝑛

Raising the Power of index notation

¿¿ Example 1: simplify ( = =