AJAX stands for "Asynchronous JavaScript and XML." It is a set of web development techniques used to create asynchronous web applications. While XML was commonly used in the past, JSON is more prevalent today for data interchange in AJAX requests.

You can add a new property to a JavaScript object by simply assigning a value to a new property name. For example, myObject.newProperty = 'some value';. While you can use methods like Object.assign() to copy properties from one object to another, it's not used for adding new properties. There's no Object.addProperty() or addProperty() method.

In JavaScript, the prototype property is a reference to an object from which the current object inherits properties and methods. When you access a property or method on an object, JavaScript first looks for it on the object itself and then, if not found, on its prototype. Understanding prototypal inheritance is crucial in JavaScript.

In JavaScript, the ** operator is used to exponentiate a number. For example, 2 ** 3 evaluates to 8, as it calculates 2 raised to the power of 3. This operator was introduced in ECMAScript 2016 (ES6) to provide a concise way of performing exponentiation.

The innerHTML property in JavaScript is used to access the content of an HTML element. It allows you to retrieve or modify the HTML content within the element, including any child elements, text, or HTML tags.

To strictly compare the inequality of two operands without type coercion in JavaScript, you should use the === operator. This operator checks both the value and the data type of the operands. In contrast, the == operator performs type coercion and may not provide the desired strict comparison.

The capture parameter in the addEventListener method is used to specify the event phase during which the listener should be triggered. When set to true, the listener is triggered during the capturing phase, and when set to false, it is triggered during the bubbling phase. This parameter helps control the order of event execution.

To insert an HTML element as the first child of a parent element, you should use the prepend() method. This method adds the element as the first child, making it the top element within the parent. appendChild() adds it as the last child. insertBefore() requires specifying a reference node. createElement() creates an element but doesn't insert it.

In event handlers, such as those in JavaScript for the web, the "this" keyword typically refers to the DOM element that triggered the event. This behavior allows developers to access and manipulate the specific element that triggered the event, making it a powerful feature in front-end web development.

To handle different mathematical operations (+, -, *, /) based on user input in a calculator application, it's best to create separate case statements for each operation within a switch statement. This approach is clear and maintainable, allowing you to perform the corresponding calculation for each operation. Using regular expressions within a single case or converting the input into a numerical expression unnecessarily complicates the code. An if-else statement is less idiomatic and less efficient for this purpose.