RULES
- The definition of something being raised to a power is just being that it is multiplied by itself as many times as the exponent requires. Ex. 2^3 = 2 * 2 * 2 = 8
- When you have a power with a power you must multiply the exponents. Ex. (x^4)^12 = x^48 How is was done: (x^4)^12 take the power that x is raised to and multiply it with the power the parenthesized equation is: 4 x 12 = 48 48 is the number that the parenthesized equation is raised to.
- When multiplying powers with the same base, you add the exponents. Ex. x^4 * x^7 = x^11 How this was done: x^4 * x^7 take the two (or more) exponents and add them together: 4 + 7 = 11 Once you get the exponent, you raise it to the base, which is x (in this equation, you get x^11
- Distributing the exponent through out each variable. This relates to rule one. You distribute the exponent and add it to each other exponent to get the answer. Ex. (5x^3st^2)^2 = 25x^6s^2t^4 This may look confusing, but no fear! Lets pick it apart: take each variable or number and distribute the exponent. 5^2 = 25 (x^3)^2 Remember to multiply the exponents and you should get: x^6 For S since there was no corresponding exponent the answer is: s^2 And lastly (t^2)^2 multiply the exponents and the answer is: t^4 If you put all this distributing together, the answer to this equation is: 25x^6s^2t^4
MORE EXAMPLES
(z^x-1 / z^2) ^3 = z^3x-3 / z ^ 6
-Just remember to distribute throughout fraction!
(-8z^4)^2x = -8^2 z^8x = 64z^8x
-Don't forget rule # 3 when doing this problem!
Some Exponent Websites
Where to look in the book!
Page 161 Chapter 4 Section 1
Mr. Exponent here to save the day...
=^.^=
Wednesday we reviewed how to solve and absolute value equation and inequalities. I will show one example to refresh your minds.
Ex. 1/2|d| + 5 (greater than or equal to) 2|d| - 13
How to:
- Subtract 1/2|d| from both sides
- You should be left with: 5 (greater than or equal to) 1.5|d| - 13
- Add 13 to both sides
- Now you should have: 18 (greater than or equal to) 1.5|d|
- Divide 1.5|d| from |d|
- Now: 18/1.5 (greater than or equal to) |d| OR 12 (greater than or equal to) |d|
- Since d is absolute value, 12 can either be negative or positive thus getting two answers: d (less than or equal to) 12 or -12
This problem is found on pg. 73: 30
There are many other problems on page 73 in our textbook that you can practice your ability to solve absolute value equations and inequalities.
Great post Christian,
ReplyDeleteI really liked the way you made the most important parts of the rules in red font because it made them easier to find. The rules themselves were very helpful and the links to the other websites had lots of good information. I also liked the example you did.
This is a very well organized and informative post, Christian. Your rules and definitions were very clear and were extremely easy to understand thanks to the simplicity and how straightforward they are. Anybody who did not understand these rules beforehand would most definitely understand them after reading this. I also thought that the examples under each definition/rule are great examples of how each rule works. The pages numbers that you added for problems of the same nature are also going to be very helpful for future reference when studying for a test or quiz.
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ReplyDeleteAwesome! I really liked this post. It was easy to understand and remember the key facts from the classes. I really liked all the different media and ways to go past what we did in class.
ReplyDeleteThat was a very clear and well thought out post. You clearly separated each day so it was easy to see what we covered on each day. Your review of exponent laws was a nice refresher as were the links you provided. In your example in the second half of your post covering Wednesdays, class each step in solving the problem was clearly described and it was easy to see exactly what happened at each step. Nice Job.
ReplyDeleteChristian your post was very good! I like how you clearly outlined the rules of exponents, and how you showed then in examples. It was also helpful that the two days were clearly split up because the topics were different. Nice job!!
ReplyDeleteChristian, your post is accurate and thorough. I like that you outlined exponent rules and clearly showed how to apply each one. Explaining why each rule works would have enhanced that section and given the reader some insight as to why the rules work. Your examples were involved and you did a nice job of breaking down all the steps for simplifying each one. It's clear you have a solid understanding of how to apply the rules. My only suggestion here would have been to use Notability or Explain Everything to write your solutions since it's hard to see what is happening with only keyboard symbols. Your website resources are excellent, and Mr. Exponent himself is entertaining. Finally, your solution to the absolute value equation was well done and written out clearly with easy to follow steps. Again, a screen shot from Notability might have helped with the notation, but overall you managed well using the keyboard. Overall, nice job.
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