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Module 1 section 2
Exploration 2
Exponents

Standard Form: The regular method of writing any number

Exponential Form: A method of writing a number using exponents. The exponent tells how many times you multiply a number (base) by itself
(base) 34 (exponent)

Exponent: the raised number: in the above example it is the 4. It can also be referred to as a power of the base number. Three to the fourth power.
Base: The larger bottom number: in the above example it is the 3.

34 means multiply three by itself, four times. 3333 = 81

34 is the exponential form. 81 is the standard form.

When using exponents in patterns we also use a term table to predict the pattern. If you notice that the pattern does not increase by a constant number you are most likely dealing with an exponent. See the term table below for an example:
 
Term Number (n) 1 2 3 4 10
Term (t) 3 9 27    

By looking at the pattern above, you can see that the difference between terms changes, so you are most likely dealing with and exponent. I notice that if I keep 3 as the base and use the term number as the exponent I get the term.
t=3n
In this case the exponent is the variable. Look at the example below for a different type of pattern. The 4th term is 34=81 and the 10th term is 310=59,049
 

Term Number (n) 1 2 3 4 10
Term (t) 1 4 9    

In this case the base is the term number or variable and the exponent is always 2.
t = n
2
The 4th term is 42=16 and the 10th term is 102=100