Six rules of the Law of Indices:

To manipulate math 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 4⁵ and 9⁷ as their base differs (their bases are 4 and 9, respectively).

Rule 1:

Rule 2:

Rule 3:

Rule 4:

Rule 5:

Rule 6:

Example for 6 rules of the Law of Indices

Example for Rule 1:

Simplify 2⁰

Example for Rule 2: 

Simplify 2^-2

Example for Rule 3:

Simplify

Example for Rule 4:

Simplify 

Example for Rule 5:

Simplify (y²)⁶

Example for Rule 6:

Simplify 125^2/3