Exponents Definition and 268 Threads

I have this problem to simplify with positive exponents: \[\left[(-4a^{-4}b^{-5})^{-3}\right]^4\] So, working with the interior brackets, I applied -3 to the equation, which resulted in: \[-(-64)x^{12}b^{15}\] **because "-4" was not in brackets, the exponent was applied to the 4 only...

Homework Statement solve. .2y^3 + .6y^3 - .5y^3 I believe the answer to be .3y^3 Homework Equations The Attempt at a Solution i got the answer to be .8y^3 - .5y^3 = .3y^3 I think this is correct, I'm not sure, please let me know if I finished this correctly.

Hello everyone, I have stumbled across a curious question while programming. To start the process, say I have a a positive integer greater than one: α0 Nesting that in an exponent is a simple operation and a common occurrence: α0α1 (α1 is also a positive integer greater than 1. In fact...

Evaluate each of the following without using the calculator. how to evaluate without even using calculator?

proportional ratios with exponents - Need Help! A walker's speed, v, is proportional to the ratio of his leg length, L, and the period of the repeating motion of his legs, T, that is, v ∝ L/T. If the period is measured to be proportional to Lp, where p = 4/5, what power of L must the speed be...

Find the value of \sqrt{-\sqrt{3}+\sqrt{3 + 8 \sqrt{7 + 4\sqrt{3}}}} the options are 1 , 0 , 2 , 3

What will be the remainder when 2^256 is divided by 17 ? I tried expressing 2^256 as 16^64 and seeking a pattern between the remainders of the multiples of 16 when divided by 17 , but that didn't work

Homework Statement Simplify the expression completely 3(y)(1/3)-3x(y)(-2/3)(2x) / [(y)(1/3)]2 The Attempt at a Solution My attempt is totally wrong. I can't quit figure out what to do or where to start 3(y)(1/3)-3x(y)(-2/3)(2x) / [(y)(1/3)]2 3(y)(1/3)-6x(y)(-2/3) / y(2/3)...

Homework Statement I am working on a physics problem, and am unsure of my math at one point. The physics problem is irrelevant, as I just want to verify my math. I am in calc3 and diff eq., I am just a little fuzzy/unsure of my algebra sometimes. Could someone please tell me if the work I have...

Homework Statement Factor x + 5+ 6x^-1 Factor x^(3/2) + 2x^(1/2) - 8x^(-1/2) Homework Equations None given. The Attempt at a Solution I have tried factoring normally, it's just not working out though (for either part of the question.) I've never had to deal with this in a math...

-2((1/((x^2 + 1)^2 )) - ((4x^2 )/(x^2 +1)^3 )) = 6x^2-2/(x^2+1) This is actually the last step of this problem. I understand everything they did up until here, but I'm a bit confused as to how they got from their last step, to the actual answer. Could someone explain?

I have been stuck on two question for sometime, and would appreciate some guidance to where I am going wrong. Here are the two questions I seem to have trouble understanding. 1. 2x+5 < x-1/4 I have had numerous attempts at this equation and seem to get the answer wrong each time. The book...

Hello. I was doing algebra earlier today and I came across having to simplify log(x)\cdot log(x). Now obviously this can be described as an exponent, but I am curious how to write it. Can I write it as log(x)\cdot log(x)={log^2}(x) or should i do log(x)\cdot log(x)=(log(x))^2 I thought of this...

1.) 16 3/2 =16 1/2 =(2 square root)^3 =(2(4x4)^3 =(2 square root 4)^3

can someone help me (4a 3/2)(2a1\2) (3x5/6)(8x2/3) (27a6)-2/3 the fractions are powers

Gap exponents are denoted like critical exponents for higher derivatives of Gibbs potential. \Delta_l' (\frac{\partial G}{\partial H})_T=G^{(1)}\propto (1-\frac{T}{T_c})^{-\Delta_1'}G^{0} (\frac{\partial^l G}{\partial H^l})_T=G^{(1)}\propto (1-\frac{T}{T_c})^{-\Delta_l'}G^{l-1} \alpha'...

Hello, I can't seem to wrap my mind around this. I understand exponent properties, but for some reason when you throw that n in there it rocks my world. I was solving an induction problem, and a piece of the algebra that I sort of guessed at was this: (3n-3n-1) Which after factoring becomes...

\frac{(xa+b)a-b}{(xa-2b)a+2b} I figured since there is one addition and one subtraction of the same amounts in and out of the brackets, they would cancel each other out leaving just \frac{x}{x} which would be 1 (or possibly x?) but I really have absolutely no idea. also, and this is a...

I tend to forget some of the trigonometric functions and someone showed me how to derive the double angle identities from what I think is Euler's formula: e^{ix} = \cos x + i\sin x = e^{i2x} = \cos 2x + i\sin 2x = (e^{ix})^{2} = (\cos x + i\sin x)^{2} I have a question about this step...I...

how would I simplify or figure out i^{i^{i..}} this keep going an infinite tower of i's

Okay, I'm doing an advanced functions course online to get into Physics for university. I got this question in the exponents section... (2x3y7)5/(2x2y5)7 Intuition (BEDMAS) tells me to divide out what's IN the brackets (2/2 , x3/x2 , y7/y5) , and then the exponents outside the brackets...

Homework Statement e^2x * e^2 Homework Equations The Attempt at a Solution Really, I'm just a little bit confused on how I would go about adding the exponent. None of the examples in the book cover that. Is it simply e^2x+2?

General Question: I don't have a good grasp of what it means to use a non-rational exponent, such as xe or xi. For irrational powers, the best I have is to look at xe (for example) as a series xn where n converges to e using rational n's. That's an analytical approach that feels right, but...

The Rushbrooke inequality: H=0, T\rightarrow T_c^- C_H \geq \frac{T\{(\frac{\partial M}{\partial T})_H\}^2}{\chi_T} \epsilon=\frac{T-T_c}{T_c} C_H \sim (-\epsilon)^{-\alpha'} \chi_T \sim (-\epsilon)^{-\gamma'} M \sim (-\epsilon)^{\beta} (\frac{\partial M}{\partial T})_H \sim...

The Coopersmith inequolity: T=T_c, H\rightarrow 0^+ I'm confused by few things. What means H\rightarrow 0^+? And what difference will be if H\rightarrow 0^-? And what means T=T_c if we can't measure T_c in experiments? Then there is relation M \sim H^{\frac{1}{\delta}} That means if I...

Hi, I have recently started learning about complex numbers and the complex plane, and there is something I don't quite understand. Why is it that for every number z \in C e^{i\theta} = z we have \sqrt { [Re(z)]² + [Im(z)]² } = 1 ? Except for \theta = \frac...

Just a quick question for you guys, I've been unable to find the answer to this. Can all real numbers be written as n^p, where p is a real number?

Hi there, Please help :) out of school for years started studying again and finding it so hard to pick up the basics again! But am trying very hard! Homework Statement Simplify the expression and eliminate any negative exponents Homework Equations (2x^3)^-2 (3x^4)^2...

Basically I am trying to find an expression that can add exponents. Here is an example, let's say we start with n=5, I need something that will calculate 5^2+4^2+3^2+2^2+1^1 by putting in whatever value for n that I choose. So far I have n^3+n^2(n-1)+n(n-1) The end, n(n-1) isn't working...

Hello. I have simple DE y' + p y^(1/2) = q --------------- y'=dy/dt p,q=constant I am confused because I tried bernoulli's method to solve and I think I exploded the universe. Basically, my initial condition of t=0,y=0 made infinity, not right. I'm not sure that method works when there...

Homework Statement Write as a single power, then evaluate: a) (-32)^3/5 x (-32)^-4/5 / (-32)^2/5 b) 4096^3/6 / 4096^2/3 x 4096^5/6 Homework Equations The Attempt at a Solution a) (-32)^3/5 x (-32)^-4/5 / (-32)^2/5 = (-32)^3/5+(-4/5)-2/5 = -32^-3/5 = -1/8 <- not sure...

This is a really basic problem and I just need some review. How do I add 2k+1 + 2k+1? This is where I am stuck 212k+212k

simplify and answer should be in positive exponents. (((4x^6)^3(4y^-8))/((2x)^4(12y^3)^2))^1/2 please help and thanks

A very logical problem. Homework Statement x5y=3z and x3y=z2-3z-2 so what is (z)xy Homework Equations No equations, just multiplication,division etc. The Attempt at a Solution let xy=a a^5=3z we can write this as a^15=(3z)^3 a^3=z^2-3z-2 also this a^15=(z^2-3z-2) and then...

I know the Cartesian product for an algebraic structure: A x B = {(a,b): a ∈ A, b ∈ B} Which naturally gives An = {(a1, a2, ... , an): ai ∈ A ∀ i} Some of the time, at least we can also have a non integer n. For example [A x A x A]2/3 = A x A. Is there any way of continuing the...

Homework Statement scientific notation I have a problem that displays the 4th root of the square root of 5.2 x 10 to the -9th power Homework Equations 4 . .... ... ... -9 ... sq rt of 5.2 X 10 4 -9 sq rt of 5.2 X 10 The Attempt at a Solution The answer I...

y=\frac{100}{100}\frac{\frac{(((100/100)^2-100*100)e^{x/(100*100)}+(100*100))e^{-x/(100*100)})-(100/100)^2e^{-x*100/100}}{100/100-100*100}}{1} http://www.quickmath.com/msolver//graphs/2011-12-06/e5/61/e2/e561e26ac85a4b1da0176565a4827772-2.png?t=1323201139 0 0 1 3.67866E-05 2 0.000113525...

Homework Statement find the derivative of: 4e^t((e^2t)-(e^t)) Homework Equations d/dx[b^x] = lnb(b^x)d/dx(x) The Attempt at a Solution I tried subtracting the two exponents in the brackets as well as multiplying it out. both wrong. Help?

I have attached an image of my question because it was a bit difficult to type. Now, my question is : What is it's value upto infinity ?

Hello everyone! My question is twofold. Firstly, how do I solve for term numbers in a geometric sequence and secondly, how do I algebraically solve for variables that are exponents? Homework Statement Given the following geometric sequences, determine the number of terms, n. t1=5 r...

Can someone explain the logic behind this? For instance if 2 to the 3rd power = 2 x 2 x 2 =8 So 2 to the 3rd power is telling me I have 2 multiplied by itself 3 times. Now how would I solve for 2 to the 1/3rd power? It is telling me I have 2 multiplied by itself 1/3 times but how do you...

Homework Statement In my Number Theory class, we learned how to calculate the value of large exponents modulo primes using Euler's Theorem. I understand how to do this with exponents larger than the value of the totient function of the prime, which is p-1, but what about when the exponent is...

Homework Statement Let p be a prime number. Prove: (a+b)^p modp = [(a^p modp) + (b^p modp)]modp Homework Equations modular arithmetic. The Attempt at a Solution I honestly haven't the slightest clue. Would induction be my best bet here? If so, when I suppose the...

Hi All, I'm doing an undergraduate project regarding QPTs for some variation of a AF Heisenberg hamiltonian. I'm a little confused about the change in relations between the critical exponents for a QPT. Some books/papers state that the quantum system in D dimensions is mapped to a classical D +...

so i need to find a,b, and c: (M^0)*(L^0)*(T^1) = (M^a+b+c)*(L^-a-3b+2c)*(T^-2a-2c) to solve i equated the exponents to that of each matching variable: a+b+c = 0 -a-3b+2c = 0 -2a-2c = 1 Is there a mathematical process of obtaining the above equations besides simply "equating" the...

I decided to take physics this year, my senior year in high school, and my teacher has decided he isn't going to explain things before he assigns us homework. Any and all help is appreciated. 1. The period T of a simple pendulum is the amount of time required for it to undergo one complete...

what does this simplify to: (-33/2)2/3 I use the exponent rules to multiply the fractions to get (-31) which comes out to -3, but the answer key says the real answer is 3. Is there something important when doing fractional exponent that I'm missing out? Thanks in advance.

I'm not sure how to differentiate y with respect to x for: y = (7x^2)^[x^2] Any ideas?

Hi, the discussions in this forum have always been a great help to me as it seems there's always someone who's answered my question. However, this time I'm still puzzled. People often talk about the sum of the Lyapunov exponents of a dynamical system (i.e. adding the exponents from each...

solve for x: x^-2 = 1/9 solve for x: x^-2 - 13x^-1 +36 = 0 I don't understand how to solve either equations.