My calculator and google calculated it differently, why? To avoid confusion, where should I put the parenthesis. This can be write in  at least 16 ways with parenthesis, but which one gives the correct value?
Does $x^{y^z}$ equal $x^{(y^z)}$? If so, why?   Why not simply apply the order of the operation from left to right? Meaning $x^{y^z}$ equals $(x^y)^z$?  I always get confused with this and I don't understand the underlying rule. Any help would be appreciated!
How do I figure out the right size font / text for a given read distance? PATH variable resets with reboot Just as the title indicates my PATH variable resets after every reboot. I read that I have to edit my bashrc file's PATH variable, but I don't have anything there that suggests anything related to the PATH variable. CSS Display an Image Resized and Cropped I want to show an image from an URL with a certain width and height even if it has a different size ratio.  So I want to resize (maintaining the ratio) and then cut the image to the size I want.  I can resize with html img property and I can cut with background-image.  How can I do both?  Example:  This image:     Has the size 800x600 pixels and I want to show like an image of 200x100 pixels   With img I can resize the image 200x150px:  &lt;img      style="width: 200px; height: 150px;"      src="http://i.stack.imgur.com/wPh0S.jpg"&gt;    That gives me this:    &lt;img style="width: 200px; height: 150px;" src="https://i.stack.imgur.com/wPh0S.jpg"&gt;       And with background-image I can cut the image 200x100 pixels.  &lt;div      style="background-image:            url('https://i.stack.imgur.com/wPh0S.jpg');      width:200px;      height:100px;      background-position:center;"&gt;&amp;nbsp;&lt;/div&gt;    Gives me:        &lt;div style="background-image:url('https://i.stack.imgur.com/wPh0S.jpg'); width:200px; height:100px; background-position:center;"&gt;&amp;nbsp;&lt;/div&gt;      How can I do both?  Resize the image and then cut it the size I want? To prove $\left|\frac{p_n(z)}{q_m(z)}\right|\leq \frac{M}{|z|^{m-n}}$ for some $M>0$ Why didn't Sauron become invisible while wearing the One Ring? I'm curious as to why Sauron is the only being/person shown wearing the One Ring who does not become invisible?   Isildur, Gollum, Bilbo, Frodo, and Samwise all become invisible while wearing the One Ring.  Why didn't Sauron become invisible while wearing the one ring?  I became interested after reading Pearsonartphoto's question asking what effect wearing the One Ring would have had on . Update to latest version of java after ppa is discontinued How can I change the Windows 7 Logon Screen wallpaper? Is it possible to create a counter just with wiring? With the new logic gates in the 1.3.1 update, is it possible to create some wiring circuit that counts how many times a trigger was activated? In other words, is it possible to make a circuit that outputs a trigger every two input triggers?  I've done some experimenting but the nature of wires and there being no intrinsic on/off state in Terraria makes it pretty counter-intuitive compared to real world logic circuits. Difference between a gerund acting as subject and an infinitive acting as a subject? I am wondering whether there is any difference between a gerund acting as subject and an infinitive acting as a subject. How to evaluate $ \lim \limits_{n\to \infty} \sum \limits_ {k=1}^n \frac{k^n}{n^n}$? I can show that the following limit exists but I am having difficulties to find it. It is $$\lim_{n\to \infty} \sum_{k=1}^n \frac{k^n}{n^n}$$ Can someone please help me? Types of books or Types of book? can anybody tell me which one of these is the correct one? I have been searching all over the internet but I have still got no answer.  Types of books Types of book Will Area 51 be supported in the app? How to derive the conjugate prior of an exponential family distribution I am trying to derive the conjugate prior of the univariate Gaussian distribution over both the mean and the precision. I know that the prior I'm looking for is the normal-gamma distribution, but the idea is to derive this result.  It seems that you can write down the conjugate prior of an exponential family distribution immediately if you represent it in the canonical exponential family form.  suggests a way to do just that. So far I have written the Gaussian probability function in this form and equated the following, but I don't see how the form of the conjugate prior is immediately obvious.  $$p(\mu, \lambda | D) \propto p(\mu,\lambda)p(D | \mu, \lambda)$$ I have a COM dll written in vb6. When I try to create a new object of a class module from this dll I get a Run timer error 430: Class does not support automation or does not support expected interface. The interesting thing is that this happens only from outside the IDE, when I am debugging from within the IDE there is no error thrown and the new object of the class is created successfully. What can be the cause?  In general I occasionally get these kind of errors in COM dlls. What is the best way to debug COM issues? How can I know the path of the dll that is being used when a program is running? Configuring ADB for Nexus 4 on Ubuntu 11.10 I'm trying to deploy and test an Android app on my Nexus 4 from my Ubuntu 11.10 computer, but ADB doesn't recognize it. I think I need the Google USB drivers, but I cannot find instructions on how to install them on Ubuntu.  How can I install the drivers on Ubuntu 11.10 so that ADB will recognize my N4? Would the One Ring even work for anyone but Sauron? Given Ohm's law, how can current increase if voltage increases, given fixed resistance? According to Ohm's law, $V=IR$ (voltage equals current times resistance).  So if the voltage increases, then the current increases provided that the resistance remains constant.  I know that Voltage or potential difference means work done per unit positive charge in bringing that charge from one point to another.  So according to Ohm's law, if the work done per unit charge increases then current will increase. How can this be true? Point out my mistakes. Show that if $n>2$, then $(n!)^2>n^n$. "Oriented" vs. "orientated" What are the origins of the word orientated?  As far as I know, the correct spelling is oriented and orientated is not an alternative spelling but an error that is in common use.  Is it for example more commonly used in a certain country or by a certain people? Is there a reason for people choosing to say or write orientated instead of oriented? How to use SSH to run a local shell script on a remote machine? I have to run a local shell script (windows/Linux) on a remote machine. I have SSH configured on both machine A and B. My script is on machine A which will run some of my code on a remote machine, machine B. The local and remote computers can be either Windows or Unix based system. Is there a way to run do this using plink/ssh?