Solving Equations Involving Rational Exponents 

patrickJMT, whoever you are. Thanks so much for getting me through the basics back in 2008 when I started College. I used your video for several years, and this video brings back great memories. You started teaching me the basics of math which led me into and through Engineering, ultimately the workforce. You have a real talent at explaining things. Hats off to you. To anyone else out there starting out in Engineering. Keep going, Engineering can be extremely fun. I wake up every morning and all I want to do is go to work.

Hi, I like your videos. On this one there is an error on the third problem. At the 2:10 mark you use the reciprocal power which is fine. However, since left side is a perfect square (x^(2/3) can be written as the cube root of x squared), one could use a positive or negative value for x. So we should write x = + or - 16^(3/2) which gives x = 64 or -64. This is also verified graphically.

you answered my question in the first sentence of your video,while my textbook could not provide the answer I was looking for. keep up the videos there awesome.

whenever i have difficulty understanding something in math and i google how to do it and see one of your videos pop up i get really excited because your videos are the best

was busy teaching today, so did not get back in time! yes, your solution is correct!

I used to freak out knowing that a math test is on it's way. This year I started to watch your videos. I can't even explain how much they have helped me. I am not the best at algebra and my math teacher goes too fast and has the worst handwriting ever. I now take math tests with more confidence. (I used to not be even be able to sleep the night before a math test!!) I am less stressed and have a better average. Another great tutorial, math savior!

@HigginbothamMath oh no! that is not picky at all! thanks for pointing this out to me, i will add some annotations about the mistake. i hate when i do this... thanks for sharing my videos with your students and keep up the hard work! you are doing noble work.

Hi, I'm a math teacher, and I love linking to your videos for my math students - you explain things very well. My only (very small) issue with this video is at about 2:15, when you take both sides to the 3/2 power, you do not add a +/-. But I can't be too picky if you've done all this work! :)

you have really helped im in algebra 2 /trig and i dont really understand it so ive been looking at ur vids . im in nys and all the teacher does is teach to the test (regents) and he goes way to fast to even write down notes, so these vids r helping a lot . Thank you so much

I have a Math final tomorrow and you just saved my life with all your videos. :) Thanks.

Oh my goodness! Thank you soooooooo much for this! I don't understand why my current teacher has to make this so complicated, because you just made it so easy! Thank you Thank you!

my goodness, what took my teacher an hour to explain, you explained in at least a minute. THANK YOU!

you're a blessing that can be found on the world wide web!!!

@patrickJMT dude thanks so much for this. my math teacher had us present a topic for our class as our final project & my friend & i chose solving equations with fractional exponents thanks to ur video i learned more & i get it now..... we present tomorrow & we're ready to go =)

omg wow your handwriting's neat and you make it so easy to understand!

hope it turned out / turns out well for you. good luck!

@dpahls1 glad to help! i have tutored many children of engineers : )

@carmelarouk i am not standing in front of a class, making you sit there. that is the difference!

@HigginbothamMath thanks, just added an annotation, hopefully people will see it.

thank you so much. I'm preparing for the math placement exam and I haven't had math in a year and a half! Thank you so much for what you do!

thanks a lot!!! I have a test tomorrow and Rational Exponents are included in my pointers for review~!!!!

I watch & appreciate your video’s more than any other lessons on the Tube. I just wish there were a way to work this type of equation using: Please Excuse My Dear Ante Sally. The closest I can come to using this rule is: 2X^1/3-5+5 = 1+5 (2X^1/3)^3 = (6)^3 8X/8 = 216/8 X=27

Very helpful, i like how you start off easy and ended with a difficult one.

Thank you so much! My teacher is old and she doesn't teach things how I like them. But you explain things in a very simplistic and satisfying manner. Thank you so much! Oh wait I said already...

@2tagalong you say too fast, someone else will tell me i go too slow. that is life.

thanks pres. obama!

awesome video this is a big help on my intermediate algebra final

What does the rule state for why in some cases you get 2 answers instead of 1? For instance, when you take the nth root for an even index, then raise the answers to a power. Is it simply just applying the principal nth root?

glad i could help you out :)

@lilmisslauren13 glad you like the vids : )

thanks this video was very helpful to me. 1 question though, how would you solve y=6-y^(1/2) ? thanks

awesome video this explained exactly what i was having problems with

Just wanted to thank you for making math easy!

Man, excelent channel! really really helpful.

What a life saver. Thanks Pat

well, you can always come here any time you need to :)

All righty. I having trouble recalling what you do with these kind of problems: 6^2/3 * 4^2/3 all divided by 3^2/3...could you do that? I need this like yesterday. Thanks.

(16^1/2)^3 do you ignore the.. +- sign here? what if you take that into account what will the answer be? Thanks :)

Thanks. I don't think my Algebra 2 text was written by human beings. In fact, I'm pretty sure it was written by soulless machines. I appreciate having the concepts explained in a way that makes sense.

The way I solve this is a bit 'overkill'! It would be easier just to multiply both sides by n^2 and turn it into a quadratic function!

Very helpful video, thanks for posting :)

TYVM, this helped me study for my test :D

doooood... go be a teacher please!! you have the wits and certainly the ability to instruct properly! i've probably learned more from your videos than all of my highschool years of algebra put together

@MrInsanity132 if y=6 & y^1/2 then replace the 6 with the y as in 6^1/2

You are a math God... and I bow down... I'm not worthy..

ur vids are sooo helpfull and rock!!!! thanks man

how do you solve for x if the exponent isn't a fraction? for example x^3=125

Thank you, that's very kind of you sir,...very helpful.

Thanks! Well done!

Don't you have to check your solutions if you raise an equation to an even power? x=1 (square) x^2=1 (square root) x=1 and -1, while -1 does not satisfy the original equation

whew, thank youuuu. now i just wish you were my math teacher, my math teacher is...urghhhh it hurts my head just to think about his lessons.

@mikala15555 happy that i can help : ) come back anytime!

so stop watching and do it the way you learned in class.

Cool red markerr :D what's the brand? :)

@23ALEJANDRA23 sorry i was not of more use to u

HI Patrick, do you have a video explaining the why we take certain steps in Algebra?

i'm just really curious mr. patrick...what is your secret that makes teaching math fun? no offense intended, but when i hear my math teacher talk, all i hear is a droning sound...but when i hear you discussing, i actually hear ACTUAL words - i don't even have to think twice about copying what you said on paper!!! i posted some of your videos on our section's group on facebook (i'm a sophomore in H.S) and my classmates commented that they already got it!! so behalf of 2nd year - St. Mark, THANKS!

Thank you so much your a life saver

um i dont get the very last part how do you cross multiply or flip the equation if the the fraction is positive? that confused me howd you get n=3/4?

Where did you get -19 from? I got -20

Hey Patrick. Quick question, how do i send you questions to your email without your email D=

@harajukugirlxx3 ah, that is nice : ) i am glad i can help you sleep at night!!

@ScorpiaStingz9595 ha, ok : )

how do you solve when the exponent is a fraction of x ? i.e. 2.75= 5,5 to 3.8/x

you're right

Lol my teacher tries to teach us but when she can't..she just opens up ur videos

Thanks

amen

Hi :) What about solving systems of equations? When both equations have variables in the exponents and different bases.... >.< I'm stuck.

Good afternoon Sir , i have a problem, hope you will help me please Sir X^2/3+x^1/3-6=0 Thanks in advance Sir

dude you saved my life

how can you solve this if there is no variable. for example: (imma use parentheses to show the exponents) 64 (1/2) + 27 (1/3).

Your really good! Thank youu :D

@patrickJMT

tell her to send me part of her paycheck

you rock

@awesomeninja241 But Patrick didn't

@ScorpiaStingz9595 ahahahaah your teacher is crazy!!!!! Does she want to lose her job? lol

Cheers

solve equation with log x and ln 4e to the power of x minus 3 = 0.. how to do?/

yes. Just plug in your answer to double check. So, 8*8 =64 64^1/2 =8 8^1/2 is a decimal not 16

Help me with solving x from 2x^5/3 - 5x^4/3

Your awesome man! :)

Cool vid.

why did he divide by two?

Thanks =)

1/n = 4/3; n = (1*3)/4

@faceownddd thnks for calling me stupid i apreciate it (and i do know i spelled it you dont have to correct me) you should probly talk to my math teacher not me i learned that months ago and now i barly remember that so its a bit hard to defend myself and thats all i have to say in answer to your harsh words

@patrickJMT Yeah, that is right....that's life. You're a real people person aren't you....lol

x^3 = 125 x = cuberoot(125) x = 5

I know this video is old, but for those that are not naturally talented in math you go way too fast. Also, you were isolating equations without explaining why,. Like when you divided everything by two. I know the reasons may seem obvious for you, but not for a few others. Thanks

i listen to music and sleep or draw and then i go to youtube to learn Math :D my teacher explains everything way too fast

he did it wrong when you do the inverse power the signs switch so 1/3 the inverse isnt 3 its -3

left handed ftw!

@carmelarouk whoa, i used up all 500 characters on my comment :)

@ScorpiaStingz9595 in the near future......youtube will become school!!!!! :)))

Complete

Why, hello, you are my new best friend. :) I am like...math-retarded. Lol. So this will help me out a lot. /sub.

@23ALEJANDRA23 I suck too. But I like math n.n

@ScorpiaStingz9595 what a terrible teacher you have.