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".
6^{2} can be read as "6 raised to a power of 2" or "6 squared".
4^{3} 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:


• 4^{3} = 4 × 4 × 4 (the 4 is being used as a repeated factor)
• 12^{7} = 12 × 12 × 12 × 12 × 12 × 12 × 12
12^{7} is in "exponential form"
12 × 12 × 12 × 12 × 12 × 12 × 12 is in "expanded form"
• 8^{1} = 8 (any number raised to a power of 1 is equal to itself)
• 6^{0} = 1 (any number raised to a power of 0 is one, but 0^{0} is undefined)
• 5^{3} = 5^3 (this is an alternate notation often seen on computers and calculators)
• 10^{5}
= 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 in^{3} 
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 a^{5}.