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Module 1: Basic Concepts - Exponents
Introduction
Exponential Notation
Objectives
- Express numbers in exponential form.
- Solve equations involving exponents.
Exponents and logarithms are used extensively in the air pollution field since many chemical and physical processes can be described using these notations. For example, the hydrogen ion concentration of liquids is expressed as pH; the vapor pressure of compounds in air is expressed using the log 10 form; and the efficiency of electrostatic precipitators can be estimated using an equation in which all of the unit sizing terms are presented as an exponential function. Exponents and logarithms are a type of shorthand for expressing very large and very small numbers.
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#1 - What is the exponent in the mathematical expression 103?
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#2
- What does the notation 63 mean?
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#3
- What does the notation 6-3 mean?
In summary, exponential notation takes the form, Bx, where B is the base and x is the exponent. The exponent is a real number that can be positive or negative. The number B is raised to the "x" power.
TIP: The exponent can be a fractional number such as +1.23 or
3.4.
In this case, the value of the expression is found by using the yx
function key on a scientific calculator. The base value, "y,"
is entered first, followed by the exponent, "x."
Practice Problems
Exponential Notation
- Instructions:
- Complete the Practice Problems before proceeding to the next section. Click on the button below.
When adding and subtracting numbers raised to the same power, the exponent
is unchanged as illustrated in the following general formulas:
- Where:
- Example Problems
The general formula for multiplying numbers with exponents is shown in the following equation:
- Where:
- Example Problems
The general formulas for dividing numbers with exponents is shown in the following equation:
- Where:
- Example Problems
The general formula for raising a number in exponential form to a power is shown in the following equation:
- Where:
- Example Problems
Practice Problems
Mathematical Operations
- Instructions:
- Complete the Practice Problems before proceeding to the next lesson. Click on the button below.