1. The n-th power of a number is calculated by multiplying the number n-times with itself.
2. Instead of repeatedly writing the number that is multiplied n-times with itself, the exponential notation is used. This notation consists of two components the base and the exponent. The exponent tells you how many times the base is multiplied with itself.
3. When dealing with very large numbers in mathematics or physics it is usually impractical to fully write out these numbers, instead the exponential notation can be used. In this notation the number 3,000 can be written like 3 * 10^3, because the 3rd power of 10 is 10 * 10 * 10 = 1,000 and multiplied by 3 the result equals 3,000. To illustrate the usefulness of this notation here is an example from physics: the estimated number of atoms in the universe is 1 * 10^80 atoms. This number is made of a 1 followed by 80 zeros.
4. Instead of repeatedly writing down the multiplication of the base x with itself, you would simply write the exponent in superscript next to it. In this example the exponent is 5, so you would write it like this: x^5
