What is an Exponent?
Definition:
Here are some examples:
27 can be represented as 33
Did you know that this is same as 3 multiplied by itself 3 times?
27 = 33 = 3 x 3 x 3
32 can be represented as 25
You guessed right, this can also be represented as 2 multiplied by itself 5 times.
32 = 25 = 2 x 2 x 2 x 2 x 2
1,000,000 can be represented as 10 6
That is a short way to represent 10 multiplied by itself 6 times.
10 6 is really 1,000,000. Remember:
1,000,000 = 106 = 10 x 10 x 10 x 10 x 10 x 10
10 6 = 1,000,000
http://cs.gmu.edu/cne/modules/dau/algebra/exponents/exp1_frm.html
An exponent is a number that tells how many times the base number is used as a factor. For example, 42 indicates that the base number 4 is used as a factor 2 times. To determine the value of 42, multiply 4*4 which would give the result 16. Squares indicate that the exponent has a value of two. The term square comes from the geometrical shape that has the same width and length. To find the area of a square you would multiply the width times the length.
Exponents are written as a superscript number (e.g. 42).
Some facts about exponents:
- Zero squared is zero (e.g. 02 = 0)
- One squared is one (e.g. 12 = 1)
http://www.aaastudy.com/exp-eval-squ1.htm
Exponents are shorthand for multiplication: (5)(5) = 52, (5)(5)(5) = 53. The "exponent" stands for however many times the thing is being multiplied. The thing that's being multiplied is called the "base". This process of using exponents is called "raising to a power", where the exponent is the "power". "53" is "five, raised to the third power". When we deal with numbers, we usually just simplify; we'd rather deal with "27" than with "33". But with variables, we need the exponents, because we'd rather deal with "x6" than with "xxxxxx".
http://www.purplemath.com/modules/exponent.htm
Rule 1: To multiply identical bases, add the exponents.
Example 1: means
which in turn can be written . According to Rule 1, you can get to the answer directly by adding the exponents.
Rule 2: To divide identical bases, subtract the exponents.
Example 1: can be written
which can be written as
or
The later can also be written . According to Rule 2, you can get to the answer directly by subtracting the exponents
Rule 3: When there are two or more exponents and only one base, multiply the exponents.
Example 1: can be written . According to Rule 1, we can add the exponents. can now be written . According to Rule 3, we could have gone directly to the answer by multiplying the exponents
http://www.sosmath.com/algebra/logs/log3/log3.html
Rules of Exponents |
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