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
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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 = 1
00,000   (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)

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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


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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

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For calculator help with exponents
click here.

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