1. Negative and Zero Exponents

2. Definition of Negative Exponents
(let a be a nonzero number and let n be a positive integer)
The expression a-n is the reciprocal of an.
a-n = a ≠ an
1 = an
a-n
3-2 = 1 = 32

3. The negative exponent says the number needs to be moved to the opposite location and made positive.
If it’s negative in the numerator, it belongs in the denominator position positive.
If it’s negative in the denominator position, it belongs in the numerator position positive.

4. Definition of Zero Exponent
(let a be a nonzero number and let n be a positive integer)
A nonzero number to the zero power is ALWAYS 1!
a0 = 1 a  0
30 = 1
(x2y5)0 = 1
The expression 00 is undefined.

5. Simplify expressions: write with positive exponents.
1 (-5)3 =
(-5)-3 =
24 ∙
244-3 =
= 24∙ =
-3-4 =
= -

6. Simplify expressions: write with positive exponents.3
3a-3b-2 =
a3b2 1 1
(3-3)2 =
3(-3 ∙ 2) = 3-6 = = 36
729