This Blog exists for the collective benefit of all algebra students. While the posts are specific to Mr. Chamberlain's class, any and all "algebra-ticians" are welcome. The more specific your question (including your own attempts to answer it) the better.
I don't understand #6. 2a(-4)b(0) (numbers with parentheses are exponents). All the examples show a number with a negative exponent at the end. When it's at the front of the expression, does it remain the same like when it's at the end or is it different?
The first step would be to substitue in the variables: 2(2)^-4(-4)^0 --> (2)1/16(1)(when your are multiplying by the exponent of 0 the answer will always be x1). I learned a great trick to helping solve negative exponents. take 2^-4 for example. in order to solve, you simple change the exponent to a positive and make it a fraction by putting one over it (1/^4). the answer would be 1/16. In this problem you multiply 1/16 by two and you get 1/8 or .125, which is your final answer
I have a question about the explanation on pg 416.. Problem 4... If you substitute -3 as the exponent for 2^(-3), how would you get 1/8? Wouldn't it be 1/6?
To second anonymous, no it wouldn't. It wouldn't because you would turn 2^-3 into 1/2^3. 2^3 is equivalent to 2x2x2 or 2x2=4 4x2=8. Since 2^3=8 it would be 1/8
Ya know what folks, I would be just as happy if you didn't do the homework... PLEASE do not stress, it will ALL make sense after tomorrow's lesson... relax and enjoy your evening, ok?
(you'll never hear me say that again, so you might as well enjoy it while it lasts!!)
Number 11 and number 12 look similar, but there not. Actually they are opposite.
#11 (-5)^-2 1/(-5)^2 1/25 is your final answer.
#12 -5^-2 -1/-5^2 negative sign next to 1 goes next to the line between 'em -1/25 negative sign next to 1 goes next to the line between 'em
Earlier in the year we learned that (-5)^2 is different than -5^2
(-5)^2 or -5^2 is really (-1*5)^2 or -1*5^2
Remember, YOU NEED TO FOLLOW PEMDAS So, (-1*5)^2 is equal to (-5)^2 which equals 25 But in -1*5^2 you have to do exponents first because there are no parentheses. So you'd then get -1*25, which, simplified, is -25.
But, of course with negative exponents it is 1/-5^2 so you just turn the -25 that I got above into 1/-25, which Mr. Chamberlain prefers to be either -1/25 or the negative sign in the middle.
I know everything was probably very confusing. I had trouble with this in the beginning and actually i don't know if you were in the class when Mr. Chamberlain taught us that lessons.
WOW! That is a very difficult question to answer in narrative. Great job, Julian, I think you did better than I would have.
Not to worry if you are still confused, Paul. We will straighten it out tomorrow.
The problem is, you have a test to take. Can you take the test before school either tomorrow or Thursday? We can't do it after school due to the early dismissals and parent conferences.
I don't understand #6. 2a(-4)b(0) (numbers with parentheses are exponents). All the examples show a number with a negative exponent at the end. When it's at the front of the expression, does it remain the same like when it's at the end or is it different?
ReplyDeleteThe first step would be to substitue in the variables: 2(2)^-4(-4)^0 --> (2)1/16(1)(when your are multiplying by the exponent of 0 the answer will always be x1). I learned a great trick to helping solve negative exponents. take 2^-4 for example. in order to solve, you simple change the exponent to a positive and make it a fraction by putting one over it (1/^4). the answer would be 1/16. In this problem you multiply 1/16 by two and you get 1/8 or .125, which is your final answer
ReplyDeleteAren't numbers 11 and 12 exactly the same?
ReplyDeleteI have a question about the explanation on pg 416.. Problem 4... If you substitute -3 as the exponent for 2^(-3), how would you get 1/8? Wouldn't it be 1/6?
ReplyDeleteTo second anonymous, no it wouldn't. It wouldn't because you would turn 2^-3 into 1/2^3. 2^3 is equivalent to 2x2x2 or 2x2=4 4x2=8. Since 2^3=8 it would be 1/8
ReplyDeleteI have a question about #6, too. Because the Negative exponent is on top, does that mean there will be a fraction on top?
ReplyDeleteOhh.. Thanks Paul. I'm getting it mixed up with multiplication!!
ReplyDeleteOh & for #7, wouldn't it also be repeated multiplication??
ReplyDelete#7 would be repeated division because you turn the number and it's negative exponent into a fraction and a fraction is really division.
ReplyDeleteYa know what folks, I would be just as happy if you didn't do the homework... PLEASE do not stress, it will ALL make sense after tomorrow's lesson... relax and enjoy your evening, ok?
ReplyDelete(you'll never hear me say that again, so you might as well enjoy it while it lasts!!)
So no Homework? YAY!!!!!
ReplyDeleteYup... I think it might be better that way.
ReplyDeleteYay!
ReplyDelete(I will enjoy this now..)
Paul,
ReplyDeleteNumber 11 and number 12 look similar, but there not. Actually they are opposite.
#11
(-5)^-2
1/(-5)^2
1/25 is your final answer.
#12
-5^-2
-1/-5^2 negative sign next to 1 goes next to the line between 'em
-1/25 negative sign next to 1 goes next to the line between 'em
Earlier in the year we learned that (-5)^2 is different than -5^2
(-5)^2 or -5^2 is really (-1*5)^2 or -1*5^2
Remember, YOU NEED TO FOLLOW PEMDAS
So, (-1*5)^2 is equal to (-5)^2 which equals 25
But in -1*5^2 you have to do exponents first because there are no parentheses. So you'd then get -1*25, which, simplified, is -25.
But, of course with negative exponents it is
1/-5^2 so you just turn the -25 that I got above into 1/-25, which Mr. Chamberlain prefers to be either -1/25 or the negative sign in the middle.
I know everything was probably very confusing. I had trouble with this in the beginning and actually i don't know if you were in the class when Mr. Chamberlain taught us that lessons.
Let me know if you have any more questions.
-Julian
Come on!!!!!!!!!!!!!!
ReplyDeleteI just took 20 minutes writing that lesson for Paul and now you tell us you're going to explain it tomorrow!!!!!!!!!!
WOW! That is a very difficult question to answer in narrative. Great job, Julian, I think you did better than I would have.
ReplyDeleteNot to worry if you are still confused, Paul. We will straighten it out tomorrow.
The problem is, you have a test to take. Can you take the test before school either tomorrow or Thursday? We can't do it after school due to the early dismissals and parent conferences.
Let me know... send me an email if you can.
Mr. C.
Question #6 anonymous,
ReplyDeleteYes. At some point in the simplification process you will end up with a fraction in the numerator.
You will get...
2(1/2^4) as the numerator
1 as the denominator
You can simplify that down to...
2/16 as the numerator
1 as the denominator
Which ends up being 2/16, simplified down to 1/8, which should be your final answer.
-Julian
Mr. C, I have to take a test. Why?
ReplyDelete-Julian
Julian is correct again with #6, although there are a number of different ways to look at that (and other) problems.
ReplyDeletePaul has a test to take, not you Julian!
Again, for anyone confused about the homework, just take the rest of the day off and we'll see you in the morning!
Oh ok, just wanted to make sure.
ReplyDeleteI think I should get a beanie baby for my detailed explanations!!!
perhaps?
ReplyDeleteHaha I just knew Julian would say that.. And thanks for the help!
ReplyDeleteBy the way, Mr.C, is your "favor" due on Friday?
The packet vs. textbook thing?
Anonymous,
ReplyDeleteYes. The packet v. textbook thing is due on Friday.
Yes, I would say that.
-Julian
Actually, since I gave you the night off on homework, why not get it to me tomorrow (if you can... no stress, of course!)
ReplyDelete