THE LAW OF Indices

Indices and the Law of Indices

Indices in maths is used to refer to numbers that has a multiply of itself in an exponential form. In plain English, indices are a number with a power. The index of a number shows you how many times to use the number in a multiplication.

A simple example of index is am; where a is the base number and m is the power.

Indices are also regarded as powers of numbers. It defines a number that shows how many times a number multiplies by itself.

You should know about these following points before we proceed further with indices.

1. Index plural form is called an indices

2. Index can be interchanged with power or exponential

3. Indices rules apply when the base numbers are the same.

Now let’s define a real indices example below

7 x 7 = 72 = 49

The indices above show that 7 is the base number while 2 is the index of the 7.

In maths, the concept of indices can be understand and easily apply with laws of indices. There are about six laws of indices and we are going to look at each one. But before we proceed, we will have a glance at the entire laws.

Indices are a valuable way of more conveniently expressing large numbers. They as well offer us with a lot of useful properties for influence them with the use of what is known as the Law of Indices.

What are Indices?

The expression 25 is defined as follows:

25 = 2 x 2 x 2 x 2 x 2

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

To influence expressions, we can reflect on using the Law of Indices. These laws merely apply to expressions with the same base, for instance, 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 varies (their bases are 3 and 5, correspondingly).

Six rules of the Law of Indices

Rule 1:

a0 = 1

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

An Example:

Simplify 20:

a0 = 1

Rule 2:

 a-m = 1/am

An Example:

Simplify 2-2 = 1/4:

Rule 3: a-m x an = am+n

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

An Example:

5 x 53

Simplify : (note: 5 = 51)

5 x 5 x 5 x 5 = 625

Rule 4:

a-m ÷ an = am-n

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

An Example: 5(y9 - y5)

Simplify

 5(y9 - y5) = 5y4

Rule 5:

(am)n = amn

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

An Example:

Simplify (y2)6: = y12

Rule 6:

am/n = n√am

An Example:

Simplify 1252/3:

1252/3 = 25

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