The discovery of exponents gave us the capability to communicate certain mathematical concepts in a much faster and more efficient manner. You have seen the use of exponents as they applied to powers of 10. Now, let' take a look at exponents as they are applied to whole numbers in general.

The exponent of a number indicates how many times to use
that number under multiplication. 
exponentpic2
In this example, 6 is called the "base" and 2 is called the "exponent".

Exponential Notation
Expanded Notation
Standard Notation
62
66
36

The word "exponent" is often synonymous with the word "power".
62 can be read as "6 raised to a power of 2" or "6 squared".
43 can be read as "4 raised to a power of 3" or "4 cubed".

The base value is a number being used as a "repeated factor".
exponentpic
lookup
The use of an exponent is referred to as repeated multiplication.   38

Remember that multiplication is referred to as repeated addition .  38

Important Concepts:
  • 43 = 4 × 4 × 4     (the 4 is being used as a repeated factor)

• 127 = 12 × 12 × 12 × 12 × 12 × 12 × 12
          127 is in "exponential form"
          12 × 12 × 12 × 12 × 12 × 12 × 12 is in "expanded form"

• 81 = 8     (any number raised to a power of 1 is equal to itself)

• 60 = 1     (any number raised to a power of 0 is one, but 00 is undefined)

• 53 = 5^3     (this is an alternate notation often seen on computers and calculators)

• 105 = 10 × 10 × 10 × 10 × 10 = 100,000   (remember when working with powers of 10,
    the exponent becomes the number of zeros in the standard notation)

• ex34    (the base value can be a fraction, or even a decimal)

• anto    (n multiples of the value of a)

divider dash

Exponents and Units of Measure:

When working with units of measure and exponents (or powers),
remember to adjust the units appropriately:

(25 in)3    
 = (25 in) • (25 in) • (25 in)

= (25 • 25 • 25 )(in • in • in)

= 15625 in3


divider dash


Examples


1. Write this expression in expanded form and then evaluate: (5.2)3

(5.2)3 = 5.2 x 5.2 x 5.2 = 140.608

2. Write this expression in exponential form and then evaluate: 34th

34thA

3. Write seven cubed in exponential, expanded, and standard forms,

73

4. Explain the difference between 5a and a5.

5a

divider dash


ti84c
For calculator help with exponents
click here.

divider

NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation
 and is not considered "fair use" for educators. Please read the "Terms of Use".