Department of Mathematics

Pindling Basic Algebra   by Example Series

Key Concept: Learn the properties of integer exponents so that you make use it to manipulate equations.

Skills to Learn:

1. Know the basic definitions of exponents identities

2. Know the properties of exponents

3. Know the operational order of exponents relative to other operations

4. Know how to use exponents to evaluate expressions

5. Know how to manipulate exponents involving Scientific Notations

6. Know how to use Scientific Notations to Simply Computations

Basic Definitions with Examples (n are any integer)

Concepts	Definition / Expression	Example(s)
Power Functions	, n times , n times Bases are x and a Exponent is n	Show that
Exponent 1, n =1
Zero Exponent,
Negative Exponents,

Basic Properties of Exponents with Examples

Concepts	Example(s)
, same base	Simplify Simplify
, same power	Simplify Simplify
, power of exponent	Simplify Simplify
Quotient Properties of Exponents	Simplify Simplify without negative exponents

Order of mathematical operations:

First ( ), then Exponents, then Multiplication / Divisions and then Addition / Subtractions

Simplify the expression: Evaluate ( ) first : , then exponents , then [ ] , then Multiply , then add

Simplify the Expression: Group like terms - same base or

Scientific Notation ( )

Standard Notation	Scientific Notation
123,870	1.2387 x 105
0.0135	1.35 x 10-2
5.25	5.25 x 100 (remember that 100 = 1)

Examples of Scientific Notation Calculations:

Use Scientific Notation to Simplify: , group exponents , ,

Use Scientific Notation to Simplify:

Show that is