#simplify each expression using a single exponent

131 messages · Page 1 of 1 (latest)

toxic creekBOT
somber python
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Which one is it specifically that your having trouble with?

quartz folio
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what did you do for 9? 13 is similar to that one

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oh. you said you were having trouble with those 2, so i assumed you did the others

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okay. do you think you have the ability within yourself to do number 2?

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if you can do that one, 5 will follow much more easily

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ah, i think the top of the page has the addition law for exponents on it?

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that will help a lot

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yeah. at the center left of the grey box, it says "Law of Exponents for Multiplication"

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then this law says that if you have some number a and some exponents m and n, then a^m + a^n = a^{m + n}. this law will simplify problem 2 if you can identify what a, m, and n should be in this specific case

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monkaHmm. do you know how to add numbers?

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thats all you need for this

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also subtraction, later

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okay we are basically the same then peepoHappy

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i think if you read the first box, it will help explain what's going on here. when we write 5^4, it is shorthand for 5 x 5 x 5 x 5

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so if you have like 5^3 x 5^2, this is the same as (5 x 5 x 5) x (5 x 5)

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and then thats the same as 5 x 5 x 5 x 5 x 5

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and then you can write that in the short way as 5^5

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so this shows that in this specific case, 5^3 x 5^2 = 5^{3 + 2} = 5^5

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the law just below that part says that this holds for all numbers, not just 5 and 3 and 2

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so your goal is to take this powerful law and apply it to more specific cases to simplify them. it's like how we have a law that says gravity pulls things toward the earth; specifc cases of that law are when i drop a ball or trip and fall down or something

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i think you wrote six 5's

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it should be 5x5x5x5x5

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peepoHappy yeah

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yeah. that's how people usually type it

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since there's not an easy way to type tiny superscript numbers

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number 2? yeah you would type it 9^9 x 9^4. i don't have • on my keyboard lol but i can copy and paste yours

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so 9^9 • 9^4

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yeah

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yeah

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they just have more symbols. but they are just as simple as the others FeelsOkayMan

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the entire worksheet will be applying the general law(s) at the top to specific cases

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hahaha

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i mean i guess you can do this if you want to, but i feel like you will get further behind in math for the rest of your life

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unless you use the power sparingly 😶‍🌫️

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rotate your phone sideways

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the iphone calculator is a little bit garbage though, so you're probably just going to be more confused

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if you want to calculate 3^3, press "3", then press x^y on the left, then press "3" again

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and then press =

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probably use no calculators. wait how old are you

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hmmm. you have two paths. do things the hard way where you learn what to do and solve it with your mind or turn to the dark side of using the calculator. if you go the second route, it becomes much harder to leave it as time goes on

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and then there will probably be a day later on where you wish you knew more math, but now you have to relearn everything they taught you since you were 14, and then you will be heavily discouraged

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its probably easier to slowly keep up with the material. it's not so bad. they give an example of how to apply the law under each law they give at the top

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it seems like you haven't written anything. what's the main mental block that you're having

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yeah that makes sense. probably extra hard to focus on this if you don't find it enjoyable. i've known many math people with adhd, but they enjoyed it very much (or were medicated).

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maybe like a highly simple example will help

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can you simplify 3^2 x 3^1

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no, but you should explain how you got that so i can help correct you

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also, i'm looking for an answer in the form 3^n for some number n

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i guess first of all, 729 = 3 x 3 x 3 x 3 x 3 x 3. writing out so many 3's might make it more clear why someone invented this exponent notation

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its 9^9

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lol. yeah they really made it so you can't use a calculator

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probably in your best interest for them to have done that

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you have to apply the law at the top of your page

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it works for all numbers, you just have a specific instance where you can apply it

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since you have specific numbers here

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yeah, you can do that to solve the problem, but its going to be worse than applying the law

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but yeah, 9^9 = 9x9x9x9x9x9x9x9x9 and 9^6 = 9x9x9x9x9x9, so 9^9 x 9^6 = 9x9x9x9x9x9x9x9x9x9x9x9x9x9x9

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yeah

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that's good, it's important to know that

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so then you know what things like 9^9 mean

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but the law just under it to the left is what you want

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it works by expanding them out, its just that if you notice when you expand 9^9 and expand 9^6 and multiply them together, you get a lot of 9's. how many 9's? well you first wrote 9 and then you wrote down 6 more, so in total you have 9 + 6 9's

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and this is what "Law of Exponents for Multiplication" says

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you can find these sites, but it will be ultimately worse for your life to use them at this point

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if you can do the entire worksheet then it makes more sense to use a site like this

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since it's just saving you time--it isn't causing you to lose out on understanding

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what time is it there

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i feel like you have time. if you can just comprehend what the laws are saying, things will go very quickly. certainly the first 2 lines will

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yeah, i guess so. 3,4, and 5 will be the same. but i mean i might as well just demonstrate number 1 lol

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it's the exact same thing

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4^2 x 4^3 = 4^{2 + 3} by the law

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with a = 4, m = 2 and n = 3

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replacing those symbols with those numbers

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you could also do 4^2 x 4^3 = (4 x 4) x (4 x 4 x 4) = 4 x 4 x 4 x 4 x 4 = 4^5 by expanding

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but when you write down two 4's then three more 4's and count them all, you're just doing 2 + 3

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so you might as well apply the law and save yourself from counting tons of symbols

quartz folio
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by applying the law described at the top of the page with a = 9, m = 9, n = 4

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like how did i know n was 4?

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yeah. bad combo for the adhd

hard belfry
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hi

quartz folio
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i'll help periodically i guess for as long as i'm on the computer peepoHappy

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you just convert it back into exponent notation

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since 3^n means 3 x 3 x ... x 3, where there are n 3's

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you just compactify it back up by counting the 9's

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i feel like you missed a number or something

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you can't, you can sort of simplify the expression with the distributive law, but it doesn't get much simpler in any general way

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yeah

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you can go as high as you want

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9^928374908123740918237409128374

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pog

worn patio
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a^b*a^c=a^(b+c)

quartz folio
worn patio
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rules of exponents

quartz folio
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i've tried FeelsStrongMan

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yeah, but you would type it 9^{9 + 4}

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or 9^(9 + 4)

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you want 9 + 4 to be in the exponent position

worn patio
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a*b =/= b+a

quartz folio
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that's just the way you type it on the computer. otherwise it's confusing

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since you don't have good access to superscripts

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you can't tell if 9^9 + 4 means 9^(9+4) or (9^9) + 4

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they're also just a number

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so you don't have to worry about them. you just do the law to -5

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yeah the law says (number)^{another number} x (number)^{another another number} = (number)^{(another number + another another number)}

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-5 is a number, so you don't have to be concerned at all

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oh i meant x

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another symbol for it. lol

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i think it tells you at the top of the page

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yeah. it says "negative exponent" and tells you what that means

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it is a fraction with denominator a

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so 2^{-1} = 1/2

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5^{-1} = 1/5

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they give the example of 3^{-2} = 1 / (3^2) = 1 / (3 x 3) = 1/9

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what confuses you? in the example of 2^{-1}, i am saying that we have this collection of symbols "2^{-1}" that we write down on a piece of paper. when we do that, we are referring to the number 1 / (2^1) = 1 / 2

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and then by replacing 2 with some arbitrary symbol a, i can describe what i mean by all expressions in the form a^{-1} where a is a number

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i don't know how better to explain it. i feel like it will just get more and more into philosophy of math, do mathematical objects exist, how do we use symbols to represent objects and other ridiculous topics

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it seems strange that it's so difficult. you are currently stringing together tons of symbols in a way that obeys grammatical rules in order to communicate with me

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which isn't very trivial at all

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oh, rip. that explains it i guess. but still, i feel like the only difficult thing to do here is to interpret what the laws mean, and they are given in terms of symbols

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not that long, but it's been awhile

quartz folio
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ah i only started at 4:50, your time

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its 6 for me

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i feel like it will be a good exercise to discover a website that can do this on your own

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you have what you want the website to do, and you have google to help you find it

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use this one

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