Posted In: KS3

Indices Meaning:

  • Indices are a helpful method for all the more just communicating huge numbers. They are otherwise called forces or types. 
  • In the numerical procedure of exponentiation, a base number is composed nearby a superscript number, which is the exponent. 

Indices Explanation:

  • Indices clarify what number of duplicates of the base number are increased. For example, a base to the second power is alluded to as the base squared and shows that the base is increased without anyone else's input once. A base with a file of 3 is alluded to as base cubed. Exponential expressions are frequently expressed as a number to the force of its record. For example, 3 to the fifth power. 
  • The procedure of exponentiation is administered by an arrangement of standards known as the laws of records, or type laws. The principles incorporate the idea that any number other than 0 is constantly equivalent to 1 if its list or example is 0. Another decide holds that to separate numerical expressions that have a similar base, it is important to duplicate the base and subtract the types.
  • Exponentiation is utilized as a part of numerous zones of concentrate other than math, including science, software engineering, material science and science. It is likewise utilized as a part of commonsense applications, for example, figuring progressive accrual and foreseeing an expansion in populace.

The expression 25 is defined as follows: 

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


Indices Laws:

To control expressions, we can consider utilizing the Law of Indices. These laws just apply to expressions with a similar base, for instance, 34 and 32 can be controlled utilizing the Law of Indices, however we can't utilize the Law of Indices to control the expressions 35 and 57 as their base varies (their bases are 3 and 5, separately).

Indices Rules:
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 2^0:


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  : (note: 5 = 5^1)

Rule 4: 


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

An Example:



Rule 5: 

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

An Example:

Simplify (y^2)6:


Rule 6:

An Example:

Simplify 125^2/3:



For more information, you can watch the below video



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