## Chem – Exponents

One representation or function that a lot of people can be unfamiliar with is the exponent. Simply put, exponents are causing a chain of multiplication events. For example, 10 with an exponent of 6 (looks like this: 106 or 10^6) means that you take 10 and multiply it by 10, 6 times in a row. The formula is: 10*10*10*10*10*10. Exponents can also appear with a negative in front of them, like 10-4. The formula for this one is: 10 / 10 / 10 / 10. So they are the opposite of each other. If you have a positive exponent, you multiply, and if you have a negative exponent, you divide. If you are unsure how to input exponents into a calculator, then go to this page: VIDEO How do I put exponents into my calculator? The link in previous sentence includes demonstrations of the examples below.

Numerical exponents should only be shown as a number in the upper position next to other numbers. Exponents will not be shown next to letters of elements (this is a charge which we will discuss in a later lesson). So for an example of what I mean, you can write 54 and that is an exponent. However, if I write out S-2, that is not an exponent.

Examples: Provide the answers for these exponent problems.  VIDEO How do I put exponents into my calculator?

 22 = 2*2 4 56 = 5*5*5*5*5*5 15625 6-3 = 1 / (6*6*6) 1/216

Exponents will be used throughout chemistry, but they are usually very common when it comes to a concept called which will be discussed in the next lesson. In scientific notation, the focus is on exponents of 10, as illustrated in the examples below.

Examples: Provide the answers for these exponent problems

 103 = 10*10*10 1,000 10-4 = 1 / (10*10*10*10) .0001 105 = 10*10*10*10*10 100,000

You can input these problems into your calculator and work them out that way, but as you get further into chemistry, you might want to use a trick to make finding exponents of 10 faster and easier for you. This trick involves moving the decimal to the right or left, depending on if it is a positive or negative exponent. If it is a positive exponent of 10, then you move the decimal to the right however many spaces the exponent number is. In the previous example of 103, You start off with 1.0 : if you move the decimal to the right once, you get 10 : if you move the decimal to the right again, you get 100 : and if you move the decimal to the right yet again, you get 1000. How many times did we move the decimal? Answer: 3. That is because the exponent was 3.

PRACTICE PROBLEMS: Give the regular (non-exponent number) for the exponent problems below problems.

 10-2 .01 106 1,000,000 109 1,000,000,000 10-7 .0000001  