Embedded Files
Lesson Objectives
Recognize an exponential Expressions and apply the appropriate rule when multiplying and devinding exponents with similar bases.
Powers
Powers
A product in which the factors are identical is called a power of that factor. For instance...
32 = 2 × 2 × 2 × 2 × 2, so 32 is the fifth power of 2.
Exponential expressions
Exponential expressions
Exponential expressions are just a way to write powers in short form.
The exponent indicates the number of times the base is used as a factor.
So in the case of 32, it can be written as 2 × 2 × 2 × 2 × 2 = 25, where 2 is the “base” and 5 is the “exponent”. We read this expression as “two to the fifth power”.
In general, we will have an = a × a × a... × a (n times),
where a = base and n = exponent, this read it as “a to the nth power.”
Other examples in which exponents are used to show powers are given below.
- 42 = four to the second power (or 4 squared) and means 4 × 4, or 16.
- 103 = ten to the third power (or 10 cubed) and means 10 × 10 × 10, or 1000.
- a6 = sixth power and means a × a × a × a × a × a.
NOTE: A number raised to the first power is that number.
For example, 101 = 10.
To show the factors of a number expressed using exponents, you write the number in “expanded form”, also called factored form.
Activity 1
Activity 1
Activity 2
Activity 2
The product of two exponential expressions with the same base is given as:
am . an = am + n
Keep the base and add the exponents
For example, 32 . 33 = a3 + 2
• Definition If a 6= 0 then we define a 0 = 1 This definition is needed in order to add exponents consistently. For example, a 2 = a 2+0 = a 2a 0 implies that a 0 = 1.
If a is a non-zero real number, then the quotient of two exponential expressions with the same base is shown to the right
Rule: Keep the base and subtract the exponents
Power Rule, or Power Law, is a property of exponents that is defined by the following general formula:
(am)n = am . n
In words: Keep the base and multiply the exponents.
Page updated
Google Sites
Report abuse