#EXPONENTS

[brightgreendandelions]

A post about math

do you ever get confused why you can't raise negative one to a fractional exponent? if we try, we can two get different results for the same expression:  

this is all because there are two (2) different "power" operations taught to you in school. wow. one works by repeated multiplication, and the other is defined thru natural logarithms 0_0

let's go thru the process of inventing it from scratch. so if we want to repeatedly multiply something, we just need a multipliable number and a counter to count the multiplications. it doesn't make sense to multiply zero or a negative number of times, so the exponent has to be a nonzero natural number. but we can easily extend it to all integers, if our base is also dividable and has a multiplicative identity (i.e. it's a member of some Field). i'll just take the real numbers for now.

but extending to real exponents is a bit harder. it doesn't make any sense to multiply something a fractional number of times. so we have to rely on the exponent "product rule": when you multiply two numbers, their exponents add.

if you do some tricky math (which i don't remember shhhh), you can prove that the only function, that satisfies this relationship, is e to the x (or exp for short). we can now use it to expand our definition to all numbers, for which we can define The Natural Logarithm (epik). but that doesn't include negative numbers at all. so the previous definition is still useful.

if you're feeling extra fancy, you can even use this infinite sum definition for exp. this way our exponent can be literally anything even vaguely resembling a number. like a matrix, for example :)

here's an example of how you can (but probably shouldn't) use this knowledge. the matrix powers here are actually different operations

#math #numbers #exponents #mathblr #textpost #longpost #tumblr just ate half my post wtf #don't press ctrl+z when writing a long post #you're going to have a heart attack #latextpost

[gamr4evr200]

Fucking MATH!!!

#mathematics #math #exponents #pattern #what the fuck #wtf #fuck math

[greetings-inferiors]

How cold I am = a*e^(b*number of socks I am wearing)

#maths #math #mathblr #mathematics #models #modelling #exponents #exponential #randyposting #textpost #shitpost

[math-journal]

Tricks

2nd one

Change of base

#algebra 2 #a2u3 #logarithms #exponents

[anhometech]

Mastering Exponents in Google Docs: A Step-by-Step Guide

Introduction to Using Exponents in Google Docs Exponents play a crucial role in various fields such as mathematics, science, and engineering. They are used to denote repeated multiplication of a number by itself, simplifying complex expressions and making calculations more manageable. Whether it’s for solving equations, representing scientific notation, or calculating growth rates, exponents are…

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#Exponents #Google Docs #Mathematical Notation

[fktutorials-blog]

Simplifying Exponential Equations

Laws of exponents can be used to simplify exponential expressions

The laws of exponents include the product rule, the quotient rule, the power of power rule among others.

According to the product rule, when two powers of natural numbers multiply, pick one base and add the exponents.

Here are some two examples:

2³×2⁴=2⁷

5²×5³×5⁴=5⁹

With the quotient rule, we pick one base and subtract the exponents.

Examples include:

3⁴÷3²=3²

9⁷÷9³=9⁴

10⁵÷10=10⁴

Here is an example on the power of power rule.

(2²)³=2⁶

(6⁵)⁴=6²⁰

Please, watch this YouTube video about two students applying the laws of exponents to simplify an exponential expression.

One applied the rules wrongly, while the other did it correctly.

#exams #teaching #education #teacher #school #exponential #exponents #mathematics #math #indices #product rules #Youtube

[division-duplex]

exponent rules

including negative exponents

im not fully understanding it yet but im starting to be able to remember the rules for negative exponents at least..!

#study post #exponents #math rules

[mathhombre]

Power Up

One of my favorite of the games I've made. A mini-RPGish exponents game. For Mathober Day 27: Power, I came up with a new character.

The game was for middle school, 5-8, and the writing and drawing drew engagement from kids that weren't interested in more strategy-based games. Read more in this old blog post.

MaxiMum

Dr. Maxine Cervantes, leading expert in particle physics, had a lab accident, which resulted in her tiny frame taking on a highly variable density. This gave her super strength. (4^x) She developed a rolling attack to use her high density and low center of gravity to power through any opponents (3^x). If things get desperate, she can uncork - returning to normal density by growing to a size even she can't even predict (x^y) for 5 minutes before she snaps back to superdense. When it came time for a codename, her kids were ready: MaxiMum was ready to save the day!

Anybody ready to battle!?

#mathober #mathgame #exponents #MaxiMum

[newzzwired]

Pele, One Of The Finest Exponents Of The 'Beautiful Game', Dies Aged 82

Pele, One Of The Finest Exponents Of The 'Beautiful Game', Dies Aged 82

Named athlete of the century by the International Olympic Committee in 1999, Pele is the only footballer in history to win three World Cups — 1958, 1962 and 1970. #Pele #Finest #Exponents #039Beautiful #Game039 #Dies #Aged https://sports.ndtv.com/football/pele-one-of-the-finest-exponents-of-the-beautiful-game-dies-aged-82-3649461#rss-sports-football

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#039Beautiful #Aged #dies #Exponents #Finest #Game039 #Pele

[howlingwolf23]

So random patterns i have noticed while looking at the exponents of 2

Every group of 3 numbers will be same number of digits, every 0 number resets to back to first number being 1, the last digit will always be in the order of 2,4,8,6, every group of 10 will be an increase of 1000, and finally the first digit follows a very similar pattern to the first set of 10.

For example 2, 4, 8 (one digit) 16,32,64 (2 digit) 128, 256,504, (3digit) and then at 2 to the 10th power resets back to 1 for 1008 and then after that, it will begin again at 2^11 for 2016.

So by knowing this set of facts you can roughly know the first and last digits and how many digits in the answer lol (this is what I think about when I can't sleep)

#story time #funny #math #cant sleep #do math #exponents #exponential

[tellmemoreabouttesl]

Dad's Worksheets

Dad’s Worksheets

November 17th, 2020  Hello there, everybody! How are you doing? Keep hanging in there, you’ve got this! I’m cheering for you all! Given the fact that this post is due for 2024, I really hope that everything is doing well. We are all, by the time of this post, almost three months into the year 2024, is it going well? Is it not going well? I have a lot of hopes that the world will be doing somewhat…

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#Addition #Additions #Algebra #division #Divisions #Exponent #exponents #factorization #flash card #flash cards #Fraction #Fractions #Long division #long divisions #mean #median #mode #money word problem #multiplication #Multiplications #negative #negative number #negative numbers #percentage #percentages #pre-algebra #Subtraction #Subtractions #Telling Time #Time

[justinempire]

Exponents

#Exponents

[yet-another-haven-of-dollya]

I want his dick...

no lube, no protection, all night, all day, from the kitchen floor to the toilet seat, from the dining table to the bedroom, from the bathroom sink to the shower, from the front porch to the balcony, vertically, horizontally, quadratic, exponent al, logarithmic, while i gasp for air, scream and see the light, missionary, cowgirl, reverse cow girl, doggy, backwards, forwards, sideways, upside down, on the floor, in the bed, on the couch, on a chair, being carried against the wall, outside, in a train, on a plane, in the car, on a motorcycle, the bed of a truck, on a trampoline, in a bounce house, in the pool, bent over, in the basement, against the window, have the most toe curling, back arching, leg shaking, dick thribbing, first clenching, ear rining, mouth drooling, ass clenching, nose sniffling, eye watering, eye rolling, hip thrusting, earthquaking, sheet gripping, knuckles cracking, jaw dropping, hair pulling. teeth jitterbug, mind blogging, soul snatching, overstimulating, vile, sloppy, moan inducing, heart wrenching, spine tingling, back breaking, atrocious, gushy, creamy, beastly, lip bitting, gravity defying, nail biting, sweaty, feet kicking, mind blowing, body shivering, orgasmic, bone breaking, world ending, black hole creating, universe destroying, devious, scrumptious, amazing, delightful, delectable, unbelievable, body numbing, bark worthy, cant walk, head nodding, soul evaporating, volcano erupting, sweat rolling, voice cracking, trembling, sheets soaked, hair drenched, flabbergasting, lip locking, skin peeling, eyelash removing, eye widening, pussy popping, nail stractching, back cuts, spectacular, brain cell desolving, hair ripping, show stopping, magnificent, unique, extraordinary, slendid, phenomenal, mouth foaming, heavenly, awakening, devils tangos, he could put a nuclear bomb inside me and i'd still ride.

-🐹 anon

Today on another episode of "What the fuck did I just receive in my ask box?"

#“quadratic exponent al logarithmic”??? + - × ÷ π √ ??? #Why do you have a goddamn dicktionary??? #Ain't no way imma read all that #Should I call for Jordan? #dollya ask #dollya art #dol pc #lya the blossom #kariya the alter ego #lyah the emancipated

[math-journal]

Mid Unit Reminder

General

(1st inside)^ (exponents 2nd)

Remember PEMDAS

Solving equations with #’s

Ex. (3x + x + y)^3 , x=1, y=2

1st (simplify)^later

(4x + y) ^3

2nd (simplified)^NOW

(4^3)(x^3) + (y^3)

3rd equation solution —> plug in

(4^3)(1^3) + (2^3)

4th solve

256 + 1 + 8

5th solution

266

#math archive #math #exponents #pemdas #elementary algebra #unit 11 #review notes

[veveisveryuncool]

WHAT DO YOU MEAN I'VE NEVER DRAWN DAROACH BEFORE????

#its rodent on the exponent for the top left lmao #not very creative on that one #anyways people SLEEP on daroach and the squeaks #hes prime sexyman material!! a rodent with a cape who evades the law!!! #AND the squeaks are canonically found family so #you know im a sucker for that #alt universe where daroach got popular instead of magolor #jkjk i just wish squeak squad was better received #kirby series #kirby #daroach #doc kirby #spinni kirby #veves ultra cool art

[merpiko]

today feels so unreal what do u mean i got hozier tickets. in general admission. the floor. my first ever concert is gonna be HOZIER. WITH FLOOR TICKETS. WHAT!!

#i love my mom btw #she helped get them for me while i was in math class and couldn't queue for them bc i needed to learn how to make radicals into exponents #hozier