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Exponents and Polynomials
Laws of Exponents
For m, n ∈ { natural numbers}
1. a m·a n = a m + n
2.
3.
4. a 0 = 1 Note: The result of raising any base to the 0 exponent
will always be 1. (a ≠ 0)
5. (a m ) n= a m·n
6.
(a·b)n = an·bn
7.
8.
[The nth root of a -- the index is the denominator.]
9.
[The nth root of the power a m -- the index is the denominator.]
Note: The alternative approach to # 2 (division of powers) would have you subtract the smaller from the
larger and place the resulting power in the position of the larger.
Under suitable conditions the exponents can be any rational number.
[The nth root of a -- the index is the denominator.]
[The nth root of the power a m -- the index is the denominator.]