ExponentsDate: 12/04/96 at 09:12:48 From: Michael Baker Subject: Exponents Dear Doctor Math, I have trouble working out exponent problems. Is there an easier way to work them or understand them? Date: 12/04/96 at 13:30:01 From: Doctor Mike Subject: Re: Exponents Hi Michael, It's great to hear from another "Mike". I'm glad you asked this because there IS a good way to figure out exponent problems. It is really such a simple idea that it's really easy to forget to do. ALWAYS KEEP THINKING ABOUT EXACTLY WHAT THE EXPONENT MEANS. For instance, say you are asked to simplify 9^3 times 3^9 which is usually written in books as : 3 9 9 * 3 but we usually write it in E-mails as 9^3*3^9 to save space. Let's start by asking what 9^3 means. It is 3 nines multiplied together, or 9*9*9. I'm sure you can figure out what that is, but we don't need to know that. In fact we need to go in the OTHER direction and break it up MORE. Since 9=3*3, we know 9*9*9 is really (3*3)*(3*3)*(3*3), which is 3*3*3*3*3*3. Now it's time to think again about the meaning of exponents to see that this is exactly the same as 3^6 or 3 to the sixth power. Right? Now we can re-write the original problem as : 6 9 3 * 3 If the goal of the problem is to simplify, then I think we have made progress, since we are now dealing with only one number raised to some exponents. But we can do more. Time again to think about what the exponent means. The left side is 6 three's multiplied together, and the right side is 9 three's multiplied together. We can actually write that out to see what it looks like: (3*3*3*3*3*3)*(3*3*3*3*3*3*3*3*3) How many three's are there? Go ahead and count them. There are 15 of them. So how can you write down that you have 15 three's all multiplied together? Yes, 3 to the 15th power or 3^15. Here I have once again just used the same old information about what the exponent notation MEANS. So, we now know that 9^3*3^9=3^15. Eventually you will start doing a lot of this right in your head, but you should always keep reminding yourself what it all means. This will be especially important for problems a lot harder than the one we just did. I hope this helps. Bye for now. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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