This document provides an overview of exponents and exponent rules, including: 1) Positive exponents represent multiplication of the base repeated as many times as the exponent, while negative exponents represent the reciprocal of the base raised to the positive exponent. 2) Any nonzero number to the zero power is equal to 1, and a negative exponent is the reciprocal of the base to the positive exponent. 3) Expressions must be rewritten using only positive exponents in algebra by applying rules for negative exponents.

1. P. 504 – Key Concepts

2. Zero & Negative
Exponents
Section 8.3
P. 503

3. Powers of Tens
Exponent,
2 1 0 -1 -2 -3
n
102 101 100 10-1 10-2 10-3
10n 100

4. Negative Exponents
Exponent,
3 2 1 0 -1 -2 -3
n
Power,
8 4 2
2n
Power,
27 9
3n
Power,
64 16
4n

5. Exponent Rules
• Let ‘a ’ be a nonzero number and let ‘n’ be a
positive integer,
A nonzero number to the zero power is 1:
a0 = 1 (a = 0)
20 = 1 (-2)0 = 1
a-n is the reciprocal of an: therefore
a-n = 1 / an , (a = 0 ) so 2-3 = 1/ 23
an = 1/a-n 23 = 1/ 2-3

6. 2 1
2 2
2
4
3
y
4
1
0

7. • In Algebra, expressions need to be rewritten
using only POSITIVE exponents.
2 3
2x y
3 4
5g h
3 3
4 4

8. 1
2
4
3
3
2
4

9. 2 2 2
(5a) 5 a
2 3
(4n )
3 2
4 x y

10. 2
2
3
1
4
4
5

11. • Assignment: P. 506 3-26
• Copy the problem, then simplify. There
can be NO NEGATIVE exponents in your
final answer.