One application of exponent properties comes from scientific notation. Scientific notation is used to represent really large or really small numbers. An example of really large numbers would be the distance that light travels in a year measured in miles. An example of really small numbers would be the mass of a single hydrogen atom in grams. Doing basic operations such as multiplication and division with these numbers would normally be very cumbersome. However, our exponent properties make this process much simpler.
First we will take a look at what scientific notation is. Scientific notation has two parts: a number between one and ten (it can be equal to one, but not ten), and a power of ten (10 raised to an exponent power).
The exponent, b, is very important to how we convert between scientific notation and normal numbers, or standard notation. The exponent tells us how many times we will multiply by a factor of 10. Multiplying by 10 in effect moves the decimal point one place. So the exponent will tell us how many times the exponent moves between scientific notation and standard notation. To decide which direction to move the decimal (left or right) we simply need to remember that positive exponents mean in standard notation we have a big number (bigger than ten) and negative exponents mean in standard notation we have a small number (less than one).
Keeping this in mind, we can easily make conversions between standard notation and scientific notation.
Convert to scientific notation 

Put decimal after first nonzero number 

Exponent is how many times decimal moved,  

Positive exponent, standard notation is big  

Our Solution  
 
Convert to scientific notation 

Put decimal after first nonzero number 

Exponent is how many times decimal moved,  

Negative exponent, standard notation is small  

Our Solution 
We can use similar thinking to convert from a number written in scientific notation into standard notation. For these types of conversions, remember that a positive exponent means a large number, and a negative exponent means a small number.
Convert to standard notation 

Positive exponent means standard notation big number. Move decimal right 5 places 

Our Solution  
 
Convert to standard notation 

Negative exponent means standard notation is a small number. Move decimal left 3 places 

Our Solution 