Exponents - Only Natural Numbers
A power is an abbreviated form of writing a multiplication formed by several equal factors.
6 x 6 x 6 x 6 x 6 x6 x 6 = 67
The exponent of a power indicates the number of times to multiply the base by itself, in the above case, 7.
Properties of the Powers of Natural Numbers
1) a0= 1
2) a1= a
3) Product of powers with the same base:
Then the exponent is the sum of the exponents.
am x a n = am + n
85 x 82 = 85 + 2 = 87
4) Division of powers with the same base:
Then exponent is the difference between the exponents.
am x a n = am − n
25 : 22 = 25 − 2 = 23
5) Power of a power:
Then the exponent is the product of the exponents.
(am)n = am x n
(85)3 = 815
6) Multiplication of powers with the same exponent:
Then base is the product of the bases.
an x b n = (a x b) n
23 x 63 = 123
7) Division of powers with the same exponent:
Then base is the quotient of the bases.
an / bn = (a / b)n
123 / 43 = 33