Exponent Definition and 212 Threads

1.) 8 3/2 =(81/2)3 =(2 squareroot 8)2 (2 square root 2x2x2)3 =(2 square root )3 =2 square root x 2 square root x 2 square root=8 (2 square root) =16 square root 2

So I understand the math, that is, how to solve these problems. But how does inverting the base cancel out the negative in the exponent? I worked out inversion to simply be a setback of 2 decimal places, e.g. 12.5% of 8 = 1, so 1/8 is .125 % of 1. But why does this nullify the negative?

I have been thinking on this topic for a while. As I have seen on various sites: 1) a^(b/c) means "c"th root of "a^b". 2) Also an even root of a negative number does not exist in real numbers. Then I want to investigate this formula: a=(-4)^(1/2) Mustn't it be equal to...

Let p be a prime. Let H_{i}, i=1,...,n be normal subgroups of a finite group G. I want to prove the following: If G/H_{i}, i=1,...,n are abelian groups of exponent dividing p-1, then G/N is abelian group of exponent dividing p-1 where N=\bigcap H_{i} ,i=1,...,n. Proof: Since G/H_{i}...

There isn't a problem here, it's an example they gave, but I don't get how you can get the answer without using logs. 2^(2x+1) = 1/32 2^(2x+1) = 2^(-5) How do they know that it's -5? Same thing for: 3^(x-1) = 27 3^(x-1) = 3^3 Is it just trial and error? I've tried a...

This is just a quick question which arose when doing an exercise, where you had to evaluate a complex exponent, az. As you know you can easily generalize exponents to complex numbers using the fact that: az = eln(a)\cdot z However, as you also know the function lnz is multivalued, i.e...

It's a pretty basic equation: x = x^u, solve for u. ln x = u ln x ln x / ln x = u u = 1 However, this solution only applies for x > 0. Is there any way we could solve this equation for all values of x?

Hi All, Can anyone walk me through this problem. This is from an old med school entry test. The answer is 81 but I can't work out how the x terms cancel. 3x(3x^ -1/3)^3 Thanks in advance John

MDS1005's question from Math Help Forum, Hi MDS1005, I hope you meant, that your answer is, \(\dfrac{1}{2}x^7\). If that is the case, your answer is correct and the given answer is wrong.\[\frac{5x^{2}}{10x^{-5}}=\frac{1}{2}x^{2-(-5)}=\frac{1}{2}x^7\]

This may be a pretty dumb question, but how is it that as the exponent value of e decreases, the rate k increases? This seems counter-intuitive, and when I enter values for e into my calculator and compare them, the higher exponents (e.g. 50 vs. 20) give higher results.

Ok, this one's got me stumped! Let's take as an example the probability density function for a random variable X so that: f(x) = \frac{4}{3x^{3}} 1≤x<2 f(x) = \frac{x}{12} 2≤x≤4 f(x) = 0 So the CDF for this variable comes out as: F(x) = \frac{-2}{3x^{2}} 1≤x<2 F(x) =...

Homework Statement z= 1+i√3 find z^9 Homework Equations The Attempt at a Solution Arg(z) = pi/3 and |z|=2 so z= 2e^i*pi/3 so z^9 = 2^9 (cos6pi +isin 6pi) = 512(1) =512 but the answer has negative 512?

Solve for x, (73/10)^(x-1)+5 - 3^(x+1)=0

I am trying to factor the following equation $$\large(x^{\frac{1}{n}}+a)^{n-1}$$ but the fact that the exponent is n-1 is throwing me off. How could I go about factoring out this equation? Thanks.

Hello, it's been a while since i did linear algebra. i need some help. I have this matrix: 1 1 0 0 1 0 0 0 0. I know the eigenvalues are 1,1,0; and that the eigenvectors will be: (1,0,0), (0,0,0) and (0,0,1). But I cannot do the jordan decomposition on the matrix i.e. write it in the form...

Homework Statement The course is Computational Physics, but in a sense this is a pretty straight computer science or even mathematical challenge. The first part of the assignment - the relatively easy part - was to write a Fortran program to take two variables - the number to which e...

What is the relation between autocorrelation and Hurst exponent in time series analysis? which are the differences and which are the similarities? thanx

How do you come up with this approximation? [1+H(t-t_0)- \frac{1}{2}qH^2(t- t_0)^2]^{-1}\approx1+ H(t_0-t)+ \frac{1}{2}qH^2(t-t_0)^2+ H^2(t-t_0)^2 Is there a rule that leads to this approximation?

Homework Statement I need to find the limit of this using L'Hopital Rule, if it exists. lim_{x\rightarrow0^{+}}(\frac{sinx}{x})^{1/x^{2}} Homework Equations All of our examples used lim f(x)/g(x)=f'(x)/g'(x) The Attempt at a Solution We have not dealt with any limits like this that have...

Homework Statement Air is compressed to 6% of its initial volume in the cylinder of a diesel engine. In the process, its pressure increased from 1 bar to 41 bar. Calculate the polytropic exponent for this process and comment on the associated heat transfer. Homework Equations PV^λ...

Definition: Proth number is a number of the form : k\cdot 2^n+1 where k is an odd positive integer and n is a positive integer such that : 2^n>k My question : If Proth number is prime number are there some other known relations in addition to 2^n>k , between exponent n and coefficient k ?

Homework Statement Compute the following sequence (show your work) (-2)n+3n ÷ (-2)n+1+3n+1 The Attempt at a Solution (-2)n+3n ÷ (-2)n(-2)+3n3n After this I don't know what to do. I know that if I can prove that something smaller than this for all n's converges to +∞, this will...

Homework Statement I have a bicycle pump where I need to calculate the pressure in a certain volume. No heat is lost during compression so this is a isentropic system initial volume is 0.3L final volume is 0.0195 Gas is air n=k Homework Equations I don't know, that's the problem...

Hi ! What does the notation mean exactly when a function has power minus one ? For example i have seen the logistic function written as: f(x) = f0[1 + exp(−βx)]^-1

Can anyone do the steps to: 4^(1+√2) * 4^(1-√2)? The book says it's 16, but I got 16^-1 steps: foil exponents: that comes out to 1-2 ? Should it not be ? then, just multiply the 4's, or do you add them?

I have been studying the exponent laws in depth and I cannot find a formal proof on this law: exp(a+b) = exp(a)exp(b) Is it formal enough to say the following? (I think not since I give an example with numbers in it) We define: a² = a*a. For example: a^8 a^7 = a*a*a*a*a*a*a*a a*a*a*a*a*a*a =...

Homework Statement As part of a problem I need to evaluate, \int^{\infty}_{0}x2e-\lambdax2 Homework Equations ∫e-λx2 = 1/2 \sqrt{\pi/\lambda} ( with integration limits from 0 to ∞ ) The Attempt at a Solution I've tried integrating by parts, also tried changing variables and...

Homework Statement \lim_{z \to 0} (\frac{sinz}{z})^{1/z^2} where z is complex Homework Equations The standard definition of a limit L'hopital's rule? The Attempt at a Solution I'm quite stumped by this one. There doesn't seem to be a way to break it down into different limits...

Homework Statement Express as z = Re[Ae^(i(\varpi t+ \alpha)] 1. z = cos(\varpi t - \pi/3) - cos (\varpit) 2. z= 2sin(\varpi t) + 3 cos (\varpi t) 3. sin(\varpi t ) - 2 cos (\varpi t - \pi/4) + cos (\varpi t) Homework Equations I used cos A + cos B; A = (a2+b2)(1/2); and tan(\theta) = y/xThe...

lim_{x->0^{+}}(1+sinx)^{\frac{1}{\sqrt{x}}} i get here 1^{\infty} form which states that's its some sort of exponent

When you have i*e^(i@) as an amplitude, when you conjugate, do both i terms switch signs? I tried this and keep getting wrong answer. Thanks in advance. BTW this has to do with spin half particles.

Explanation of a "simple" exponent rule in a derivative problem needed After differentiation, I get this : 9(t-2/2t+1)8 * 5/(2t+1)2 Now this simplifies into 45(t-2)/(2t+1)10 Now, I am wondering what the property is that combines the exponent from the top with the bottom to get an power of...

Homework Statement http://i51.tinypic.com/2zyfyaa.jpg Question 3 l ) Homework Equations The Attempt at a Solution (6a^-2b^-3)^2 (__________) 1/6a^2 * 1/b^3 / 1/2a^2 * 1/b^1 (2a^2b^-1 ) I multiplied the top half together to give me 1/ 36a^4b^2...

Homework Statement 2^-4 + 2^-6 _____________ 2^-3 Homework Equations The Attempt at a Solution Ive tried several times, I do the reciprical of all numbers ie) 1/2^4 + 1/2 ^6 ___________________ 2^3 Which gives me The wrong answer, cause i do the addiition first...

Homework Statement 2^3 / 2^0 -2^-1 Homework Equations solving using exponent laws The Attempt at a Solution i move the negetive one over and make it 2^3 /2^0 = 1/2^1 I get 8 on the left side, and 2 on the right, bring the 6 from the right to the left and get 2. The answer is...

Hello, Analyzing data from a chaotic pendulum, I calculated the Lyapunov exponent to be somewhere around 10^5 . While my gut tells me something is wrong with this number , i failed to find any information regarding the order of magnitude of Lyapunov exponents and their meaning. Can someone...

In solutions to a problem I was working on, I saw that when an expression such as e^{i\alpha} , alpha being an angle (in polar coordinates), was squared, the expression goes to unity, ie (e^{i\alpha})^2=1 But I see no reason to think that \alpha is a multiple of \pi. Could there be any other...

Getting Rid of Negative Exponent! Homework Statement So I am solving a Diff Eq ( separable equation) and I am down the the last step. After integrating both sives and solving for y I am left with y^(-2) on the left hand side. How do I finalize it and get rid of negative 2 expononent...

We were having our maths class a weeks ago and while studying quadratic equations our teacher asked us if there was an difference between x^{1/2} and \sqrt{x}. Up until then I had always assumed them to be the same thing. However he said that there was a difference and said that he would tell...

Is there a way to look at a double value in c++ and read the exponent only and put this into another variable? So if I had 3.14159x10^300 I could take 300, put it into an int Then divide 3.14159x10^300 by 1x10^(the int value)

Trying to find out the kinetic energy that a 1kg ball gives the Earth if dropped from 100 ft. I just don't know how to square a negative exponent. 4x10^-24 squared is? I was thinking it would be 4x10^-48, but I really don't know. If that is correct, would the result be different if the exponent...

Homework Statement .75 = 1 - (1 - p)^n I want to get the n alone, and find n in terms of p. Homework Equations The Attempt at a Solution I simplified it to this: 1 - p = (.25)^(1/n) Basically, I just moved numbers around. I do not know how to get the n by itself without...

I've seen the use of a negative exponent in the books and articles I've been reading lately, and I was wondering exactly what it meant. Such as 300 cm-1, where cm has a -1 as the exponent. (Dont know how to type that out.) What does it mean?

Hello Physics Forums, I read around and saw a few examples for Fermat's last theorem for exponents 1 and 2, but I was wondering if this can be proven for exponent 3. That is: Proof that IF x^3+y^3=z^3, where x,y, and z are rational integers, then x, y, or z is 0. Can this be done?

Most quantum textbooks will tell you that converting between the Schrödinger and Heisenberg pictures involves something like the following: |\Psi(t)\rangle = e^{i\hat{H}(t-t_0)}|\Psi(t_0)\rangle This does make sense to me conceptually: we define eigenstates of the Hamiltonian |E\rangle, where...

Homework Statement Use your knowledge of exponents to solve \frac{1}{2^x} > \frac{1}{x^2} Homework Equations The Attempt at a Solution x^2 > 2^x Then I am stuck. I know they intersect at x = 2.

I was trying to figure out the relation between the equation of a discharging capacitor and the Natural Inverse Exponent function v(t) = Vo*e^(-t/rc) A*e(-Ct)+B I get that A represents the voltage and the C is the inverse of the time constant but i can't figure out what the B stands for

Homework Statement f(x) = 10(sin(x))^x ----> find f '(1) The Attempt at a Solution I have tried several different approaches, but still get stuck with a wrong answer every time f(x) = 10(sin(x))^x let f(x) = y so y=10(sin(x))^x then ln y = ln10(sin(x))^x...

Homework Statement Determine the nature of the singularities of the following function and evaluate the residues. \frac{z^{-k}}{z+1} for 0 < k < 1 Homework Equations Residue theorem, Laurent expansions, etc. The Attempt at a Solution Ok this is a weird one since we've...

Homework Statement I would like to solve the following equation for the variable "n" The variable c represents any integer constant. (n/2)^n = c The goal is to get this in some form of n = ? Homework Equations The logarithm properties. The Attempt at a Solution I've tried...