The use of an exponential is a very convenient way of expressing the repeated multiplication of a number by itself. The exponent is placed to the upper right of the base number and signifies how many times the base term is multiplied by itself
When the exponent is a 2, it is referred to as squaring the term and if it is a three, it is called the cube of the term. Fractional exponents are also possible. These are generally called roots. 1/2 is the square root.
In order to add exponential terms, both the base and the exponent must be the same. Otherwise, they must be multiplied out before they can be added.
To multiply exponential terms, the bases of the terms must be the same. If the bases are the same, the exponents can be added to obtain the answer.
The rules for division are the same as the rules for multiplication of exponents. The bases must be the same and the exponents are subtracted.
If a number is very large or very small, sometimes it is easier to shorten it using exponents.
In statistics, a common term is a factorial. The factorial of a number is the product of each counting number up to and including that number. For instance the factorial of 5 is 1 x 2 x 3 x 4 x 5. The factorial of a number is noted by an exclamation symbol. So the factorial of 5 is 5! A special note is that the factorial of zero is established to equal one. Also, factorials cannot be added, subtracted or multiplied without calculating them out first. However, when dividing factorials, it can be noted that many of the terms will cancel out.