By definition, any non-zero number raised to the zero power equals
1.
2
anam
= an
+ m
To multiply numbers having the same base, add the indices. Example: 24·26
= 24+6 = 210
= 1024
3
To divide a number by a number having the same base, subtract the indices. Example: 36
/ 34 = 36–4
= 32 = 9
4
A number raised to a negative power is the reciprocal of the number raised to the positive power. Example: 4–3
= 1 / 43 = 1 / 64
5
(an)m
= an·m
If a number raised to a power is raised to a further power, the exponents of the powers are multiplied. Example: (22)3
= 22·3 = 26
= 64
6
anbn
= (a b)n
(a b)n = anbn
To multiply numbers having the same exponent of power, multiply the bases and keep the exponent.
If the product of numbers is raised to a power then each number
is raised to the power and the results are multiplied. Example: 24
34 = (2·3)4
= 64 = 1296
7
To divide a number by a number having the same exponent, divide the bases and keep the exponent.
If the quotient of two numbers is raised to a power then each number
is raised to the power and the results are divided. Example: (3 / 2)4
= 34 / 24
= 81 / 16
