Not Understanding How this Problem is Simplified

[Nogard]

Homework Statement

I'm having trouble simplifying this problem: (1000)/(∏(500/∏)^2/3)

Homework Equations

My textbook has already solved it, but I'm not understanding how they did it. They solved it as follows: (1000)/(∏(500/∏)^2/3)=(2 x 500)/(∏^1/3(500)^2/3)=(2(500)^1/3)/(∏^1/3)=2(3√500/∏)

Note: the 3 next to the √ at the end is meant to go above it. I don't remember what that's called, sorry.

I don't get how they brought the ∏ out of the denominator and I don't know where they got the 1/3 power from.

I'm probably going to have to drop out of calculus because I'm getting stuck on problems that are supposed to be cake when your at this level. Absolutely ridiculous.

 

[mfb]

Looking at the denominator only:

$$\pi \left( \frac{500}{\pi} \right)^\frac{2}{3}
= \pi\frac{500^\frac{2}{3} }{\pi^\frac{2}{3} }
= \pi 500^\frac{2}{3} \pi^\frac{-2}{3}
= 500^\frac{2}{3} \pi^\frac{1}{3}$$
Now you can combine those factors with the corresponding factors in the numerator.

Note: the 3 next to the √ at the end is meant to go above it. I don't remember what that's called, sorry.

Cubic root.
How to type mathematical formulas here

 

[Nogard]

Looking at the denominator only:

$$\pi \left( \frac{500}{\pi} \right)^\frac{2}{3}
= \pi\frac{500^\frac{2}{3} }{\pi^\frac{2}{3} }
= \pi 500^\frac{2}{3} \pi^\frac{-2}{3}
= 500^\frac{2}{3} \pi^\frac{1}{3}$$
Now you can combine those factors with the corresponding factors in the numerator.

Cubic root.
How to type mathematical formulas here

Sorry, I still don't understand. I think my algebra skills are just too weak for a course like calculus. I know you don't care, but I'll be dropping out of the class tomorrow. My strengths are in English and writing, but I absolutely hate writing and reading. I'm trying to become an accountant and calculus is a required course, but I have no idea how much of it I'll actually be using as an accountant.

 

[Mentallic]

I doubt you actually need to know how to take a derivative as an accountant, but it's the implied knowledge that you need. For example, as you're already aware, you should already know how to do this stuff if you're going to tackle a calculus class and it should become second nature for you to simplify algebraic expressions once you're done with calculus.

Similarly, that's why you're expected to complete calculus. You can't get hung up over how to do a calculation as an accountant in the same way that you can't get hung up on simplifying algebraic expressions when doing calculus.

Anyway, I don't actually have any personal experience with accounting, but that's how I imagined it should be.

 

[Nogard]

I doubt you actually need to know how to take a derivative as an accountant, but it's the implied knowledge that you need. For example, as you're already aware, you should already know how to do this stuff if you're going to tackle a calculus class and it should become second nature for you to simplify algebraic expressions once you're done with calculus.

Similarly, that's why you're expected to complete calculus. You can't get hung up over how to do a calculation as an accountant in the same way that you can't get hung up on simplifying algebraic expressions when doing calculus.

Anyway, I don't actually have any personal experience with accounting, but that's how I imagined it should be.

Alright, thanks bro. I'll probably be retaking it in the spring so before that I'll work on strengthening my algebra skills. Just a little discouraged because the business and accounting program I'm trying to get into is not going to like the fact that I got a B in Accounting I and then dropped out of calc lol.

 

[verty]

Have a look at learnerstv.com, they have very many math videos. For example, here you have 5 pages of intermediate algebra videos.

 

[Nogard]

Have a look at learnerstv.com, they have very many math videos. For example, here you have 5 pages of intermediate algebra videos.

Alright, thanks, I'll check that out.

 

[gopher_p]

I'm trying to become an accountant and calculus is a required course, but I have no idea how much of it I'll actually be using as an accountant.

I have an accounting degree and worked for a couple of years as a staff accountant, so I speak from some experience. Calculus is not likely to come up in your accounting classes or in your work as an accountant. It is used pretty extensively in statistics and economics (both micro and macro if memory serves), and you'll probably see it at least once or twice in finance. These subjects are studied by most all business students, and that is why you need to take some calculus.

This is just my opinion, but I reckon a pretty large majority of students (not just business students) who are required to take calculus don't actually "use" calculus as a regular part of their career. Some are required to use it and some need to recognize it when they see it, but most just need it so that other lecturers in other courses can use it to derive formulas without completely baffling the whole class.