Laws of Exponents

I have a question from a book I am reading but I am guessing I do not understand it since it makes no sense to me. I understand exponents just fine but I am guessing this is more of a proof question, which I am not so good at.

Prove the given Laws of Exponents for the case in which m and n are positive integers and m > n. Question a) is for Law 2 and the answer it gives is negative. I noticed when searching online that not all the rules coincide exactly, so at least in this book Law 2 is division of exponents - a^m/a^n = a^m-n. I understand the law just fine and how it works, I guess I am just not understanding the question.

Thanks for the help.

If you recognize that an exponent is repeated multiplication, the proof becomes quite simple. try and base off of that fact.

Thanks for responding.

I am reading the question as m>n, so if m/n=m-n then it would always be positive, not negative. That is what I am not understanding.

Are you sure whatever book you are using says it is negative, rather than using a hyphen? Also, does the example used have a negative number to an odd exponent? Those are the only likely solutions, otherwise a positive base would be impossible to become negative.

The question is stated exactly as in the book. The answer it gives is "negative" but examining more closely, I am not sure what it means because it gives an answer for a,b,c,d,e,f even though the Exercise only asks a question for a (Law 2) and b (Law 5).

I am linking my Public Dropbox file for this book if anyone wishes to take a look. It is for Chapter P3 which starts at page 46. The Laws start on page 48. The Exercise questions are on page 52 with the question I listed (number 97) on page 53. The Exercise answers start on page 953 on which are given the answers to the P3 Exercises, again the question at hand is 97.

https://dl.dropboxusercontent.com/u/...ometry%201.pdf

As far as I see, the answer is not in the back of the book. Also, pretty much no textbook puts proof answers in the back, just numerical answers. Unless it is a teacher's edition. I looked in the back, and there is no answer to any question 97 on the page 53. Are you swapping answers of another 97?

The proof can be discussed as under
a^m/a^n = (a*a*a*……..m times )/(a*a*a*……..n times )
= ((a*a*a*……..n times )*[a*a*a….. ( m-n)times ])/(a*a*a*……..n times ) [ because m > n ]
[a*a*a….. ( m-n)times ] = a^((m-n))

Quote:

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Originally Posted by ShadowKnight8702

As far as I see, the answer is not in the back of the book. Also, pretty much no textbook puts proof answers in the back, just numerical answers. Unless it is a teacher's edition. I looked in the back, and there is no answer to any question 97 on the page 53. Are you swapping answers of another 97?

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Page 953. Section P.3 - Page 20. Question 97 is listed with answers (a) Negative (b) Positive (c) Negative (d) Negative (e) Positive (f) Negative. Besides it being listed directly under Section P.3, both Sections P.2 and P.4 have no question 97.

But the question you were looking for starts on page 53, not page 20. The 97 answers you are reading off of are from a completely different question that stems off of the exercises starting page 20. The 97 you want answered is not in the back of the book. Look carefully.

The Page 20 thing is because that is from the physical copy of the book and the pages do not line up with the .pdf version. If you don't believe me then check all the answers before and after #97 and you will see that they line up.

If you notice, the 97 you are asking about has two parts. the 97 you are looking at in the back of the book has six parts. They cannot be the same question.

Possibly, that is why I was posting here. I said that exact thing verbatim (question having two part and the answer having five) a couple posts up.

If someone (with a better Math I.Q. than myself) could make sense of the question then explain it to me and the answer given or if not then definitively say that there was some sort of misprint.

But it would have to be some sort of misprint because that is the corresponding answer for question #97, even if it is a misprint.