Lesson
Negative exponents and Zero Exponents have special properties that allow us
to manipulate them in special ways:
1) A negative exponent can be made positive by moving the base from the
numerator to the denominator: a-2 = 1/a2 -OR- 1/a-2
= a2
[NOTE: Because we cannot divide by a 0 in Math, a ≠ 0 if a has a negative exponent.]
2) Any number raised to the zero power (except zero) is always one
(1): a0 = 1 (a ≠ 0) . . . (1287398123842698477693218)0
= 1
[NOTE: 00 = A MATHEMATICAL CATASTROPHE!!! We avoid this
confrontation at all costs and need Calculus to work through it.]
There's a proof for #2 and it is quite simple:
x3 / x3 = 1 [Any non-zero
number divided by itself is 1]
x3 - 3 = 1 [Properties of
Exponents: Division of bases implies subtraction of exponents]
x0 = 1
Therefore, anything to the zero power is 1.
Example Problems
(5645848213489487561864756189465548914564751567)0 = ?? [= 1]
(a-3b4c-1)-2
= ?? [= a6b-8c2
= a6c2 / b8-]
a-8b-2c-1
= ?? [= 1 / a8b2c]
a2b-3c4
= ?? [= a2c4 / b3]
