Stupid algebra question

[Nick1911]

(L/T²)ⁿ * T^m   =   Lⁿ*T^(m-2n)

I can't quite seem to wrap my head around why this is true, and what algebraical laws are used to derive it.  Help? 

[Nick1911]

duh, i just got it.

(L/T²)ⁿ * T^m 

(L * T^-2)ⁿ * T^m 

(Lⁿ * T^-2n) * T^m 

(Lⁿ * T^m-2n)

[RaspberrySurprise]

Algebra makes my head hurt most of the time when it's any more advanced than high school level. Even then it tends to burn a bit.

[Hawkmoon]

(L/T²)ⁿ * T^m   =   Lⁿ*T^(m-2n)

I can't quite seem to wrap my head around why this is true, and what algebraical laws are used to derive it.  Help?  

A fraction raised to a power is the same as if both the dividend and the divisor are raised to the same power. As in

(2/3)² = 2²/3² = 0.4444444444

Your formula then translates as follows:

(L/T²)ⁿ * T^m ==>

(Lⁿ * T^m) / T²ⁿ ==>

Lⁿ*T^(m-2n)

[Zardozimo Oprah Bannedalas]

This eq. looks vaguely familiar. What is it?

[Nick1911]

A simple dimensional analysis example from a book.

[Physics]

A simple dimensional analysis example from a book.

I love dimensional analysis.  My students never get why I'm such a stickler with units.  Little do they know I've solved pretty complex problems I'd never seen before, just because I knew what units the answer should be in.

[RoadKingLarry]

I squeaked through high school algebra with a C from a compassionate teacher.
I just couldn't grasp the why of it all till I got into electronics. Once
it had a purpose algebra was just another tool.

[230RN]

I was the same way with geometry, although I was pretty good at it in High School.  But I never really saw much of a use for it besides figuring out how tall a flagpole was.  Then I took Machine Shop and I finally saw what it was all about.

Hey, I'm still trying to noodle out Euler's Equation on a part-time basis.  Part-time... you know... 30 hours a week. 


http://omor.com/SF/archives/Chang12.gif


It got to be a kind of secret-password-and-countersign with a guy I know, like spies ID-ing each other before the microfilm was passed from one to the other...

"E to the eye pie," says one spy (me).

"Plus one," the other spy (him) answers with the correct countersign.

"Equals zero," the first spy (me) answers, confirming the contact, and the microfilm is passed.

We used to do that little litany as we passed each other in the hall.

[Phantom Warrior]

Algebra is awesome.  That is all.

[Nick1911]

I love dimensional analysis.  My students never get why I'm such a stickler with units.  Little do they know I've solved pretty complex problems I'd never seen before, just because I knew what units the answer should be in.

I love the concept, but am having some trouble with it.

The book uses the formula for position, based on time and acceleration as an example.

x = 0.5*at²

This, I can do.  Dimensionally;

L = (L/T²) * T²

Then!  The book notes that a more general procedure for dimensional analysis is the form:

x [proportional to]  aⁿt^m

This is where I start to get lost.  Is this a general from for ANY dimensional analysis?

[MechAg94]

I was pretty good at all that math while still in school.  Lack of use has made me very rusty. 

It wasn't until I got into college than I finally has a professor point out that the purpose of Mathematics in school is to teach you to think!  It made perfect sense as math teaches you to break down problems in to small pieces that you can then solve in logical steps and reach a conclusion.  You learn the rules of the system and use them to break up the problem and simplify it until you can get a solution.  Teaching thought is especially true when you start thinking about all the word problems everyone hated in school. 

Of course, math becomes a tool for those who use it also. 

[Physics]

I love the concept, but am having some trouble with it.

The book uses the formula for position, based on time and acceleration as an example.

x = 0.5*at²

This, I can do.  Dimensionally;

L = (L/T²) * T²

Then!  The book notes that a more general procedure for dimensional analysis is the form:

x [proportional to]  aⁿt^m

This is where I start to get lost.  Is this a general from for ANY dimensional analysis?

I've never used notation like that.  I've always just kept it in the base units.  So if I have x = 1/2 at²+V₀t, I have m=m/s²*s²+m/s*s

But, then again, I've never really thought about the theoretical structure of dimensional analysis, I just apply it when I need it.

[Monkeyleg]

I was good enough at mathematics that I tutored some students in algebra and trig. Now I don't even recognize the construction of that equation.

[don]

Physics, when I taught physics I too was a stickler for units. Once I aced a physics test and the professor asked me if I understood the problems. I replied that understanding the problem wasn't necessary. I solved all of the problems using dimensional analysis and my answers were correct.

[230RN]

Derivatives of position --I always got a yuckle out of this:

In the case of the Hubble space telescope, the engineers are said to have even gone as far as specifying limits on the magnitude of the fourth derivative.  There is no universally accepted name for the fourth derivative, i.e. the rate of change of jerk, The term jounce has been used but it has the drawback of using the same initial letter as jerk so it is not clear which symbol to use.  Another less serious suggestion is snap (symbol s), crackle (symbol c) and pop (symbol p) for the 4th, 5th and 6th derivatives respectively.  Higher derivatives do not yet have names because they do not come up very often.

(snip)

Now class, repeat after me:

Momentum equals mass times velocity!
Force equals mass times acceleration!
Yank equals mass times jerk!
Tug equals mass times snap!
Snatch equals mass times crackle!
Shake equals mass times pop!!

http://www.phys.ncku.edu.tw/mirrors/physicsfaq/General/jerk.html

Just sayin'.

[280plus]

I love the concept, but am having some trouble with it.

The book uses the formula for position, based on time and acceleration as an example.

x = 0.5*at²

This, I can do.  Dimensionally;

L = (L/T²) * T²

Then!  The book notes that a more general procedure for dimensional analysis is the form:

x [proportional to]  aⁿt^m

This is where I start to get lost.  Is this a general from for ANY dimensional analysis?

hell, I was lost way begore there.  I did nearly figure out what Hawk laid out though. The m-2n part is a bit vague but that's ok.