Exponent Basics MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts

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.

In this example, 6 is called the "base" and 2 is called the "exponent".

 Exponential Notation Expanded Notation Standard Notation

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".

 The use of an exponent is referred to as repeated multiplication.    Remember that multiplication is referred to as repeated addition .   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) •     (the base value can be a fraction, or even a decimal) •     (n multiples of the value of a)

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

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:

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

4. Explain the difference between 5a and a5.

 For calculator help with exponents click here.

 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".