10 x 10 x 10 x 10 x 10 = 100000. 105 is also equal to 100000. How are they related? 105 is much like a shortcut or abbreviation. These abbreviations are called exponents. You will note that these are five 10's being multiplied together. That is where the 5 in 105 comes from. 105 can be read as "ten raised to the fifth power." when we write 105 we mean multiply 10 to itself five times.

 
There are several special exponents. What is 61 equal to? 61 = 6. Any number or variable to the 1st power is equal to itself. Now think about 70. 70 is equal to 1. Again any number or variable to the 0 power is equal to one.

If two exponential expressions with the same base (a) are multiplied together the exponents can be added together, keeping the same base, to produce the product.
In other words:

If the bases are not the same, this property does not hold true. For example,
(35)(24) will not work.

(35) x (24)
(3)(3)(3)(3)(3) x (2)(2)(2)(2) = 3888

This does lead into another important property of exponents. What would
happen if the exponents were the same but the bases were different? Two or more exponents to the same power but different bases can be found with the following expression:
(ax)(bx) = (ab)x		  
(24)(34) = 1296
(2)(2)(2)(2) x (3)(3)(3)(3) = 1296
(2 x 3)4 = 1296

What would happen if you raised a power to a power? (23)4? Lets break this down:

There are several important things to note here. The first is 23 is multiplied by itself four times. This was then broken down even further. 23 is 2 multiplied by itself 2 times. What we end up with is four sets of three 2's, or a grand total of twelve 2's being multiplied, 212. Most importantly you should notice that 3 x 4 = 12. This means that if you have a power to a power the exponents can be multiplied and applied to the base.
          The general expression is: .

Enough about multiplication, we will come back to it latter. Lets look at this example: Do you see anything special about these exponents? Notice that if you subtract the exponents you get exponent of the solution 3-2 = 1. Just as in multiplying exponents you must remember that the for this to work the bases must remain the same. Also it is important to note that negative exponents are allowed.
          The general expression is:.

If we have different bases but the same exponents you can divide the bases and put the result to the power "n" where n is the exponent.
          The general expression is: .

Negative exponents as shown below are allowed but might introduce some confusion as to how they work. Remember we said to just add or subtract the terms as we have done in the previous examples. The best way to understand negative exponents is to see a few examples.