TOPIC 1 : INDICES

WHAT IS INDICES?

The index of a number says how many times to use the number in a multiplication.It is written as a small number to the right and above the base number.

Indices are a useful way of more simply expressing large numbers. They also present us with many useful properties for manipulating them using what are called the Law of Indices.

What are Indices?

The expression 2⁵ is defined as follows:

We call "2" the base and "5" the index

so 2 is the  base number and 5 is the index number

Law of Indices

To manipulate expressions, we can consider using the Law of Indices. These laws only apply to expressions with the same base.

for example, 3⁴ and 3² can be manipulated using the Law of Indices, but we cannot use the Law of Indices to manipulate the expressions 3⁵ and 5⁷ as their base differs (their bases are 3 and 5, respectively).

Six rules of the Law of Indices

Rule 1:  

Any number, except 0, whose index is 0 is always equal to 1  regardless of the value of the base.

A is any number for example 2 and every Index 0 is 1

Base number is 2 

Index number is 1

answer : 1

Rule 2:

An Example:

a is base of any Number and m is a indices of any number

for an example

 a is 2

m is 2

1 divide by 2 to the power of 2 

2 x 2 = 4  

Answer: 1

               4

Rule 3:

To multiply expressions with the same base, copy the base and add the indices.

An example:

base number is 5 

indices ( 1+3 ) = 4

base number X how many indices

5 x 5 x 5 x 5 = 625

Rule 4:

To divide expressions with the same base, copy the base and subtract the indices.

An example:

A is 5 

Y is the base  

and the indices is 9 and 5

(Changes Divide to Subtraction)

Indices ( 9 - 5 ) = 4

Rule 5:

To raise an expression to the nth index, copy the base and multiply the indices.

An Example:

y is the base 

2 and 6 is the indices

Rule 6:

An Example:

EXERCISE INDICES

What is the value of 6³ ?

A. 18

B. 216

C.729

D.1,296

What is the value of 2² - 2^-2 ?

A. 0

B. 3.75

C. 4

D. 4.25

What is the value of 5² + 6² ? 

A. 22

B. 51

C. 61

D. 121