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Indices are a convenient tool in mathematics to compactly denote the process of taking a power or a root of a number. Taking a power is simply a case of repeated multiplication of a number with itself while taking a root is just equivalent to taking a fractional power of the number. Therefore, it is important to clearly understand the concept as well as the laws of indices to be able to apply them later in important applications.
We will first understand the formal notation for writing a number with an index, followed by the laws governing it. So let’s begin!
Introduction
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.
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.
An Example:
Simplify 20:
| Rule 2: |  |
An Example:
Simplify 2-2:
Rule 3:
To multiply expressions with the same base, copy the base and add the indices.
An Example:
Simplify 
Rule 4:
To divide expressions with the same base, copy the base and subtract the indices.
An Example:
| Simplify |  : |
Rule 5:
To raise an expression to the nth index, copy the base and multiply the indices.
An Example:
Simplify (y2)6:
| Rule 6: |  |
An Example:
Simplify 1252/3:
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