Negative fractional exponents

2

24

New member
Joined
Apr 12, 2007
Messages
6
Hi,

What a neat find this forum is. I'm currently in a program to become a radiation therapist and this quarter is physics (math) and dosimetry (more math). It's been quite a while (years!) since I have done upper division math and I've never taken physics so this quarter will be interesting. I searched online for an answer to my question on negative fractional exponents and I seem to only be able to find either info about fractional exponents or negative exponents.

My current problem also involves "e" which it seems from class is another way to express "natural log". The equation to solve is e to the -0.0692x2/3 power. I have multiplied the numerator so now I have e to the -1.384/3 power and it seems by my notes that I should put flip the numerator with the denominator to get rid of the negative and put the "e" in the denominator so it would be 3/e1.384. Then with the calculator I get the natural log of 1.384 as 0.324977857 then divide 3 by that number and my answer is 9.231398182. Does that sound right or do I sound like I don't know what I'm doing? Thank you for your help!

K

(P.S. I read the "sticky" to new people from Ted so I will try to limit the amount of questions I may have this quarter. :) )
 
You mentioned an equation, but I didn't catch one. :?

Useful laws with exponents to know: \(\displaystyle e^{-x} = 1/e^x\)
 
24 said:
My current problem also involves "e" which it seems from class is another way to express "natural log".
Click to expand...
No. Just as "10" is not another way to express the common log (it's the base of the common log), so also "e" is not another way to express the natural log (it's the base of it).

It sounds as though perhaps a few prerequisite courses were omitted. Are you familiar with negative exponents, fractional exponents, exponential equations, and/or logarithms in general?

Note: For formatting (so we can tell what you mean by your math expressions), please follow the links in the "Forum Help" pull-down menu at the very top of the page, and learn about LaTeX or else Karl's standard web-safe formatting.

Thank you, and welcome to FreeMathHelp! :D

Eliz.
 
Seems like you're trying to evaluate the EXPRESSION (not equation) : e^(2/3 * -.0692)
(now standard to use ^ for "to the power" and * for multiplication)

2/3 * -.0692 = 2/3 * -692/10000 = -173/3750

So expression is now e^(-173/3730)

Tatoo on your wrist: a^(-p) = 1 / a^p :wink:

So expression is now 1 / e^(173/3750) which = .9549146......

......................................................................................................................

Looking at your "wording":

>The equation to solve is e to the -0.0692x2/3 power.
The expression to solve is e^(-.0692 * (2/3))

>I have multiplied the numerator so now I have e to the -1.384/3 power
That should be -.1384/3; so e^(-.1384/3)
Also, that is not a "numerator", but the value of the "power".

>and it seems by my notes that I should put flip the numerator with the
>denominator to get rid of the negative and put the "e" in the denominator so it
>would be 3/e1.384.
See what you tatooed on your wrist: that would be 1 / e^(.1384/3).
As example, if you "flip" 2, you're flipping 2/1 to 1/2.
So you don't get confused with my 173/3750: .1384/3 = 173/3750:
that step is really not required, it simply is a "better looking" fraction !

Hope that helps you some.

Once more, on "flipping":
2^(-2) = .25

1 / 2^2 = .25
 
Sorry I wasn't 100% clear

The expression (not equation) is e^ (-0.692 * 2)/3 (^ meaning power and * meaning multiplied by). So, if you look at the steps I took, maybe it makes more sense. (I'm sorry that I didn't look at the "tips for formatting. :oops: )

Regarding the "skipping of a few prerequisites", this is pretty much a crash course on physics and we are to learn what we need to know to understand the decay rate of radioactive substances, radiation as it relates to radiation therapy for cancer patients and whatever else is necessary for radiation therapists to know.

Thank you for clarifying that "e" does not stand in for "natural log". The notes we were given made it appear that it was.
 
e^(decayrate * time) is formula for remaining life of 1 unit.

In your problem, decay rate = -.0692 and time = 2/3 is my guess.
 
I appreciate the help but maybe I'm not saying things quite right. We are doing a math review of exponents, logs etc. along with starting to learn the necessary physics (we are working on speed of light and wavelength, frequency, velocity and energy of different light waves). The expression I am trying to figure out, e^(-0.692 * 2)/3, is merely one of those math review questions. It is not expressed as a decay rate problem. I think I have probably taken up too much of your time. Thank you again for trying to help me. It's been over 20 years since I did any trigonometry problems and the brain is a little slow to get warmed up to them.

K

I don't know if you are a hockey fan Denis but being from Canada, I would guess you are so I'll say "go Sens" for you. I just got home from an ECHL game. We have season tickets to the Stockton Thunder but they lost in double overtime.
 
24 said:
The expression I am trying to figure out [is] e^(-0.692 * 2)/3....
Click to expand...
By "figure out", do you mean "evaluate"?

By "e^(-0.692 * 2)/3", do you mean "e<sup>[(-0.692)(2)/3]</sup>", "[e<sup>(-0.692)(2)</sup>] / 3", or something else?

If you are evaluating, what keystrokes are you entering into your calculator? On what basis do you feel the calculator's response is not correct?

Thank you.

Eliz.
 
stapel said:
e<sup>[(-0.692)(2)/3]</sup>
Click to expand...

That's the expression on my homework that I'm trying to evaluate. The answer I got was 9.231398187 and the reason why I am questioning my answer is because I didn't know if I evaluated it correctly with my calculator. Since I was under the impression that "e" also stood for "natural log", I used that function on my calculator. Do you know the correct answer?
 
Since e is about 2.7, and since the exponent will be negative, you will have (1/2.7), roughly, raised to some power. This cannot equal 9.

Instead of using the "LN" button, try using the "e^" button.

Eliz.
 
The answer that I now have is 0.63044249 by reducing the expression to e<sup>-0.461333333</sup>

I hope that is the right answer. I will find out when I get my homework graded and returned. Thanks to everyone who tried to help me. :)

K
 
That's correct, 24.

By the way, (-0.692)(2)/3 is same as (-0.692)(2/3)

>I don't know if you are a hockey fan Denis but being from Canada, I would
>guess you are so I'll say "go Sens" for you.
Well, 24, I'm a Pittsburg Penguins fan (even if I'm from Ottawa);
ever since Mario Lemieux's 1st season with them; still am, even if he's retired.
 
Hallelujah and thank you Denis for the affirmation of my answer! And kudos to your Pittsburgh Penquins on a fine win tonight. (Go Sharks! :wink: )
 
You must log in or register to reply here.
Top