Exponents Definition and 268 Threads

Homework Statement X \geq Y > 0, find \lim_{n \to \infty} \left(\frac{2X^n + 7Y^n}{2}\right)^{1/n} Homework Equations The Attempt at a Solution I'm not really sure how to do it, but i guess I need to use the fact that \frac{Y}{X} \leq 1 , and so \lim_{n \to \infty}...

Algebra Proofs! I have two questions just to help verify what I'm doing: Let R be a commutative ring with identity. Prove that R is an integral domain if and only if cancellation holds in R (that is, a no equal to 0 and ab=ac in R imply b=c) => Suppose cancellation holds: ab=0 -> ab=0a...

Homework Statement The integral from 0 to pi/2 of 1/(1 + (tanx)^sqrt2) dx. Homework Equations trig identities? The Attempt at a Solution I tried some substitutions but it just made the problem more complicated. I also multiplied by (tanx)^sqrt2 in the numerator and denominator in...

Homework Statement Homework Equations The Attempt at a Solution Homework Statement Homework Equations u = 1+tant du = sec^2(t) dt dt = du / sec^2(t) The Attempt at a Solution It seems like I should be using substitution in the equation, however the exponent is...

Homework Statement Solve for x 5^{3x}-12^x+2^{\frac{x}{2}}=5 Homework Equations logarithm rules? log(a+b)=? The Attempt at a Solution Taking the logarithm of both sides only makes things worse from what I can see. So really, I don't know how to start. x\approx 0.386744

Homework Statement This is re-asking the question in https://www.physicsforums.com/showthread.php?t=273275" which mysteriously went quiet before the answer could be given... Anyway I also tried answering the question, but to no avail. Homework Equations a^m.a^n=a^{m+n} (a^m)^n=a^{mn}...

I have been reading a paper which introduced classical mechanics concerning only one dimension. Before we get into anything about displacement and velocity, I read about dimensional analysis. There is a section of the paper which isn't very well explained and I hope someone can explain it to...

Homework Statement Problem: Indicate whether the series converges or diverges. If it converges, find its sum. THE SERIES: Homework Equations The ratio test and w/e equation is used to find the sum of this particular series The Attempt at a Solution I was able to find...

Homework Statement Simplify. Express final answers with positive exponents. ((64m^-36)(n^-15)(p^9)) ^ (2/3) Homework Equations \sqrt[3]{} ((64m^-36)(n^-15)(p^9)) ^ 2 The Attempt at a Solution ((4m^-36)(n^-15)(p^9))^2 = (16m^-36)(n^-15)(p^9) = 1/(16m^36)(n^15)(p^-9) I...

Homework Statement \int \frac{6^x+12^x}{2^x}dx Homework Equations \int a^udu= \frac{a^u}{ln a} +C The Attempt at a Solution I don't know where to begin, I tried using parts but gave up.

ABCDEFGF is an 8-digit positive decimal integer, where each letter represents a different decimal digit from 0 to 9. The digits 1 and 9 do not appear. The nonzero even digits appear in ascending order, and the odd digits appear in descending order in ABCDEFGF. None of A and E can be zero...

Homework Statement 1. Use the method of Dimensional Analysis to show that the unknown exponents in Equation (1) are l=-1/2, m=-1, and n=1/2. Homework Equations Equation (1) is \lambda = k \mu ^{l} f ^{m} T^{n} Where: \lambda is the wavelength; f is the frequency of the sound; T is...

Homework Statement I'm taking a math of investment and credit course, in this case, solving for i which is the interest rate. My question is: is it possible to "ln both sides" of an equation? Like in (b) below, I know I could say y*ln(1+i) = ln(3). Homework Equations (a) 5(1+i)^8 +...

Homework Statement How do you solve this probem for E: E + sqrt(aE) = b where 'a' and 'b' are constants. I don't recall how to handle the exponents where you have E + aE^1/2 = b and solve for E.

If 0< s,t,u<1 then which of the following is close to s+(s+t)10^6+u10^12 1. (s+t+u)10^12 2. 10^12 3. 10^18 OR what else do u think is the answer?

I'm reading Basic Math & Pre Algebra for Dummies and it says... "As you can see, the notation 2 to the power of 4 means multiply 2 by itself 4 times." and this is written there...2 to the power of 4 = 2 X 2 X 2 X 2 = 16 Isn't that multiplied 3 times? 2 X 2 = 4 that's once. then 4 X 2...

Recently in class (11 math) we explored exponents in negatives. My teacher placed a question on the board and it said 7*1/7^-7 ( 7 times 1 over 7 to the power of -7 ) She said that in order to get rid of a negative, we must imagine that there is an imaginary "1" multipliying the fraction...

Homework Statement Can you help me simplify the following equation: -e^((-1/2)*x^2)*(x^2-1)+2*e^((-1/2)*x^2)*x. Homework Equations The Attempt at a Solution I've been guessing that you can combine the e^((-1/2)*x^2) components and thus end up with (x^2-1)x+e^((-1/2)*x^2)*x...

Homework Statement I am trying to anti-differentiate (3t+2e^t)*[e^(-3t/2)] Homework Equations The Attempt at a Solution I have simplified this into several forms, including [3t(e^(-3t/2)+2e^(-t/2)] . This form may or may not be accurate, but I am pretty sure that the form given...

I'm wondering something when you have a equation:(Of course "^" represents to the power) 4e^4(j^-3) ____________ 2d^-3(f^2) ________ 2c^2(j^-2) I know how to get rid of the negative exponents to get: 4e^4j^-3 __________ j^2(f^2) _________ 2d^3(2c^2) Question comes with...

Homework Statement 4^(x+2)=9 Homework Equations basically all I want to know is what is the best way to go about solving a problem like this. The Attempt at a Solution I know how to convert a problem as such 4^(3x)=10 using. [log(<base>4,10)]/3 = X. however I need some help with...

Hello there, This is my first post on this forum so bear with me if I don't know the rules or I am posting in the wrong area. I am coding up an of equation for a scattering rate which involve quite a few positive (and a couple of negative) exponentials which often have terms that go into...

Homework Statement Hey guys, I am having difficulty with the following problem: "If m and n are two postive integers, prove that one of m^(1/n) or n^(1/m) is always less than or equal to 3^(1/3)" Any idea of how to go about this? Homework Equations The Attempt at a Solution

I am curious, is there any way to use the binomial theorem for fractional exponents? Is there any other way to expand a binomial with a fractional exponent? I suppose Newton's theorem is not a way since it requires factorials. Thanks!

Hi I have a question about rearranging the following equation (I saw this in a finance book): If we rearrange and differentiate Z(t;T) = e^{-\int_{t}^{\tau}r(\tau)d\tau} We get r(T) = -\frac{\partial}{\partial{T}}(\log{Z(t;T)}) My question is: how do we differentiate...

Is there any way to go about simplifying this? -3x^5y^2/6x Thanks.

A population of rabbits triples every month. Assume we start out with 100 rabbits. a. How many rabbits are there after 4 months b. How long until there are 50,000 rabbits? Homework Equations ... this is where I am running into the trouble... I'm really not sure how to create the...

Ok i know this should be a relatively simple equation but i haven't done this stuff in so long i can't remember how to solve it. here goes. 4^(x+2) = 7^x +681 Solve for x I know the answer is 3 from simple trial and error but i can't show the work to prove it and i know that harder...

[SOLVED] Logarithms and Exponents Question Homework Statement 5^{x}=41 The attempt at a solution Well, I know that one way to figure this out would be that to find a common base for both sides of the equation and then use the known exponent to find the variable. The only thing...

I was just messing around on another problem I was trying to solve for someone in the homework forums when I stumbled on this: If we denote the n-th derivative the same way we do for exponents, eg the second derivative of f will be denoted by f^2, and the original function as its zero-th...

I'll not go into the details of the full question, because they are irrelevant to my problem. Basically I have to integrate \int_{0}^{\infty} exp (\iota\omega-\alpha)t dt Which is a nice and easy integration, but it's putting in the limits that bothers me. I simply wrote the exponent as...

Homework Statement I need to find the critical points of f(x) = (x^3 - 2x)e^x I found the derivative, and set it equal to zero ended up with e^x (x^3 +3x^2 -2x -2) = 0 I am having trouble factoring the second factor, any suggestions?

So I need to find the equation of the line passing through (1,∏) (∏₂,∏⁴) sorry, the two would only do sub script not super script but does represent squared. So I had to find the gradient first, so that I could then sub that along with x and y into y=mx+c but I got stuck trying to find...

[SOLVED] What's the formula for calculating large exponents? Hi! I came across the following sum and was wondering if there was some kind of formula for solving it: 16^198 Is it some kind of binomial expansion? Do you calculate the last digits first, advancing to the previous ones later? I...

limit proof?? well what i am trying to understand,actually proof is if we can get with the limit inside a power (exponent) if the exponent is irrational. Say we have any sequence (a_n) or any function f(x), let p be irrational then can we do the following, if yes why, if not why? 1...

Homework Statement 8x^-3 = 64Homework Equations None.The Attempt at a Solution I tried doing all sorts of things, changing 8x^-3 to (1/8x)^3 or trying to get both sides to have the same base, but couldn't get it to work. The book I am using does not explain how to do so, I have already looked...

Using the well-known rule for multiplying numbers raised to powers: u^{\frac{a}{b}}v^\frac{c}{d}} = (uv)^{\frac{a+c}{b+d}}, 3^{2/3}9^{7/6} = (3*9)^{\frac{2+7}{3+6}} = 27 If you can think of a better way I'd sure like to see it! :biggrin:

This was taken from a math contest a few months ago. Homework Statement xx*yy=zz find z if: x=28 * 38 y=212 * 36 Homework Equations Theres undoubtably some trick, but I have yet to find it The Attempt at a Solution Dont even think about calculator I showed my math teacher, and...

Why is it that in a formula: f(x)=2x^4...), why is it that the exponent actually BENDS the line that the fomula makes when it is graphed? I know about the high and low point in algebra two (that's what I'm taking), but i just want to know WHY does an exponent BEND the line? CD

I was just playing around in my head. I wanted to plot this graph: y=x^2.5; x=-2 This is valid right? My calc says it's invalid input.

I just started learning QM and have a question - let's say that i have the following amplitude for a particle: a*e^(-i*frequency*t) since the exponent doesn't change the probability, what is it's physical importance? from what i understood the frequency coorsponds to the energy - since energy...

so called 'hyper exponents... ...or powers or indicies' Hi, The other day I was thinking about a maths concept I've called 'hyper exponents'. adlib symbol ^^ Description of a hyper exponent. Mutiplication is to addition, as Exponents are to multiplication, as Hyper exponents are to...

Please note, there are more questions than what I'm going to give, in total I'll be giving 3. I hope to use the information with the others. 1) Homework Statement Solve the equation: 5^{1-2x} = \frac{1}{5}Homework Equations None The Attempt at a Solution I was thinking that to make live...

I always get confused when you get things like: {(-4)}^{\frac{3}{2}} or 8^{\frac{2}{3}}. Which operation do you do first and why? Do you take the square/squareroot first and then take the cube/cuberoot or what?

This is the formual Points = (PrizePool^1/2) / (PlaceFinished^3/5) Here are two examples: 266.08=(70,800^{1/2})/(1^{3/5}) 137.64=(70,800 ^{1/2})/(3^{3/5}) Now I got the first part because it's basically a the square root of the the number. But how do I do the 3/5 one? Thanks in...

Can anyone point me to a text or link that summarizes the rules when evaluating/simplifying an expression of the form (a^n)^(1/m) for a < 0. (a^n)^(1/m) yields different answers for a^(n/m) and (a^(1/m))^n . Ex: (-8)^(2/6) = (-8)^(1/3) = -2 (-8)^(2/6) = ((-8)^2)^(1/6) = 2...

I'm new here, and totally green to "real" Maths, to be nice :) But really simple question: I understand why x^1 == x, because the Identity Element of the multiplication operator is 1, so x^1 == 1*x == x, so x^0 must be just 1 on its own. (I was never told this in GCSE Maths, so I don't know...

I was never taught how to do this. How do i solve this. (x + 5)3 ? I'm thinking it's 15x? And for fractional exponenets. (-27)-2/3 =? and how do i solve for it W/O parenthesis -27-2/3 =? And if i get a mixed fractions like http://img515.imageshack.us/img515/6532/bb0fx.gif ?[/URL]

We got thirty questions dealing with zero and negative exponents, but I'm having trouble with the negative exponent questions. An example of this is: a^3b-2/3^-1a^4b^-3 (-3x^-2y^3/3^-3x^4y^8)^-2 Sorry if these two examples look messy I don't know how to write it out like people write...

These aren't homework questions. They were on a test I had today. The first was how do I factor 2x^3-3x^2-16x-5. I'm fairly certain that's right. It was actually part of a larger problem, involving finding a slant asymptote. I just used my graphing utility to find the answer, but I'd like to...