Basic Rules for Exponents:

The subsequent rules are applied to exponents.

Rule 1: To multiply numbers along with the similar base, add the exponents and remain the base the same.

a^maⁿ  = a^m+n

Example:

2²  x 2³  = (2 x 2) x (2 x 2 x 2) = 2 x 2 x 2 x 2 x 2 = 2⁵

Rule 2: While raising a power of a number to a power, multiply the exponents and keep the base the similar.

(a^m)ⁿ  = a^mn

Example:

(a²)³  = (a x a) x (a x a) x (a x a) = a⁶

that is, you multiply (a x a)  three times.  Same, for (am)n, one multiplies (am) n times. There are m values of a in each parenthesis multiplied through n parenthesis or m x n values of a to multiply.

Thus,  (a^m)ⁿ  = a^mn