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Wanna be sure this is fully correct:

So i want to add restrictions to this list of exponent laws. The code i will post now is my attempt at writing their restrictions and the laws i want to write restrictions on. SO, please let me know if my attempt is correct and if it's not i would like to see how to write them correctly.

$\mathbf{For}$ $\mathbf{all}$ $b,c\in\mathbb{R}$ $\mathbf{and}$ $\mathbf{for}$ $\mathbf{all}$ $\{a, d,d' \in \mathbb{R} | d,d'> 0\}$ $$d^b\cdot d^c=d^{b+c}$$ $$(d^b)^c=d^{bc}$$ $$(d \cdot d')^c=d^cd'^c$$ $$\left(\frac{d'}{d}\right)^b=\frac{d'^b}{d^b}$$ $$\frac{d^b}{d^c}=d^{b-c}$$ $$d^{-c}=\frac{1}{d^c}$$ $$a^{\frac{b}{d}}=\sqrt[d]{a^b}$$ $$\sqrt[d]{ab}=\sqrt[d]{a}\sqrt[d]{b},\quad\text{where} \textbf{ both } a\text{ and } b\text{ are non-negative}$$ $$\sqrt[d]{\frac{a}{b}}=\frac{\sqrt[d]{a}}{\sqrt[d]{b}},\quad\text{where} \textbf{ both } a\text{ and } b \text{ are non-negative and } b\neq 0$$ $$\sqrt[d]{\sqrt[d']{a}}=\sqrt[dd']{a}$$

Eric Wofsey
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Al3dium GD
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  • In your quotient rule near the bottom, you also need $b \neq 0.$ – Dave L. Renfro Oct 05 '20 at 19:50
  • done, anything else? – Al3dium GD Oct 05 '20 at 19:51
  • Some of the a's and b's near the bottom are not in "math mode" with dollar signs. – Dave L. Renfro Oct 05 '20 at 19:51
  • i was told that i write fro all the bases > 0 to avoid cases, but it is true that some laws work for some negative bases, but they told me too that it was too complex to add, do you have any idea for that? – Al3dium GD Oct 05 '20 at 19:52
  • edited it with your last indication, but please read what i said above, can you think of a way? – Al3dium GD Oct 05 '20 at 19:56
  • If you mean $r^s$, where $r < 0$, you are opening up a real can of worms. I advise you to consider the question radioactive unless you have a strong reason for attacking it. – user2661923 Oct 05 '20 at 19:56
  • oh right, so i shouldn't consider any < 0 as it would be too hard right? or not interested, so it is fine like that then? – Al3dium GD Oct 05 '20 at 19:57
  • if you mean any $r < 0$, re my previous comment my personal opinion is - right. – user2661923 Oct 05 '20 at 19:58
  • okay so i should leave it like that, anything else that you can catch? – Al3dium GD Oct 05 '20 at 19:59
  • One of the problems with exponent and radical conversions is that, for example, $\sqrt[3]{;;};$ is often treated in school mathematics as an operation in which the '3' is simply part of the description (like the radical sign $\sqrt{;;})$ and has little mathematical significance (i.e. '3' is treated as a symbol/label, and not as a real number that has certain properties, such as being greater than $2.875),$ whereas when $1/3$ is used as an exponent, the '3' is now treated as the number '3' and not simply as a symbol/label. – Dave L. Renfro Oct 05 '20 at 20:00
  • "anything else that you can catch?" No, I liked your work. – user2661923 Oct 05 '20 at 20:00
  • This seems to be largely identical to a previous question of yours and also this one as well as this one. Instead of re-posting, you should be refining a previous (the earliest?) instance to improve its quality. – Blue Oct 05 '20 at 20:00
  • okay thanks user2661923! – Al3dium GD Oct 05 '20 at 20:01
  • @Blue i did refined some of those but i got ignored, so i thought i created a new question, and it seems it worked – Al3dium GD Oct 05 '20 at 20:02
  • @Blue Interesting comment - does this mean that if the OP goes to an old query and edits it (re refinement), then the query goes to the "front of the hopper"? – user2661923 Oct 05 '20 at 20:02
  • exactly, i wasn't refining on some just to be sure i don't get ignored, as simply creating a new question has more chances to get answered – Al3dium GD Oct 05 '20 at 20:03
  • @Al3diumGD: "i wasn't refining on some just to be sure i don't get ignored, as simply creating a new question has more chances to get answered" ... Reposting just to get attention is inappropriate. Updating a previous attempt is the way to go, but note that making non-substantive changes just to "bump" a question to the top of the queue is frowned-upon. There's a ton of traffic on Math.SE; the community doesn't get to every question (or may simply choose not to respond). Adding clutter with reposts (especially with multiple reposts, as you have done) doesn't help the situation. – Blue Oct 05 '20 at 20:09
  • From the Mathematics Meta site: "Is it allowed to repost?". The only answer, from a Moderator, is "No. You are not allowed to do that.". Comments to the question and answer provide additional guidance. – Blue Oct 05 '20 at 20:17
  • oh okay, sorry for that, so then when a question gets edited it pops up at the top? – Al3dium GD Oct 05 '20 at 20:19
  • @Al3diumGD: Yes, edits will "bump" a question, but as I mentioned, non-substantive changes just to trigger a "bump" are discouraged. The bounty system exists to help you draw attention to questions that haven't received the attention you think they deserve. – Blue Oct 05 '20 at 20:27

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