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# definition of exponential form in math

From Wikipedia

Operation (mathematics)

The general operation as explained on this page should not be confused with the more specificoperators on vector spaces. For a notion in elementary mathematics, see arithmetic operation.

In its simplest meaning in mathematics and logic, an operation is an action or procedure which produces a new value from one or more input values. There are two common types of operations: unary and binary. Unary operations involve only one value, such as negation and trigonometric functions. Binary operations, on the other hand, take two values, and include addition, subtraction, multiplication, division, and exponentiation.

Operations can involve mathematical objects other than numbers. The logical valuestrue and false can be combined using logic operations, such as and, or, and not. Vectors can be added and subtracted. Rotations can be combined using the function composition operation, performing the first rotation and then the second. Operations on sets include the binary operations unionandintersectionand the unary operation ofcomplementation. Operations onfunctions include composition and convolution.

Operations may not be defined for every possible value. For example, in the real numbers one cannot divide by zero or take square roots of negative numbers. The values for which an operation is defined from a set called its domain. The set which contains the values produced is called thecodomain, but the set of actual values attained by the operation is itsrange. For example, in the real numbers, the squaring operation only produces nonnegative numbers; the codomain is the set of real numbers but the range is the nonnegative numbers.

Operations can involve dissimilar objects. A vector can be multiplied by a scalar to form another vector. And the inner product operation on two vectors produces a scalar. An operation may or may not have certain properties, for example it may be associative, commutative, anticommutative, idempotent, and so on.

The values combined are called operands, arguments, or inputs, and the value produced is called the value, result, or output. Operations can have fewer or more than two inputs.

An operation is like an operator, but the point of view is different. For instance, one often speaks of "the operation of addition" or "addition operation" when focusing on the operands and result, but one says "addition operator" (rarely "operator of addition") when focusing on the process, or from the more abstract viewpoint, the function +: SÃ—S â†’ S.

## General definition

An operationÏ‰ is a function of the form Ï‰ : Vâ†’ Y, where VâŠ‚ X1Ã— â€¦ Ã— Xk. The sets Xk are called the domains of the operation, the set Y is called the codomain of the operation, and the fixed non-negative integer k (the number of arguments) is called the type or arityof the operation. Thus aunary operation has arity one, and a binary operation has arity two. An operation of arity zero, called a nullary operation, is simply an element of the codomain Y. An operation of arity k is called a k-ary operation. Thus a k-ary operation is a (k+1)-ary relation that is functional on its first k domains.

The above describes what is usually called a finitary operation, referring to the finite number of arguments (the value k). There are obvious extensions where the arity is taken to be an infinite ordinal or cardinal, or even an arbitrary set indexing the arguments.

Often, use of the term operation implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain), although this is by no means universal, as in the example of multiplying a vector by a scalar.

Thus, since k can be 1, in the most general sense given here, operation is synonymous with function, map and mapping, that is, a relation, for which each element of the domain (input set) is associated with exactly one element of the codomain (set of possible outputs).

From Encyclopedia

Mathematics, Definition of

Question:so i have a problem that says... 3XaXaXaX5XyX2XaXaXaXa sorry if thats hard to read... the x's are the times sign. (not variables). so i got the answer of 3xa^7x5xYx2 is that right or wrong? am i supposed to add 3, 5, and 2 together? or leave them by themselves? or times them together? thanks for your help~

Answers:you can leave the times sign out, that way it's easier to read the answer is: 30ya^7 your answer is right, you just gotta simplify it by multiplying all the numbers

Question:what's the definition? for example i got for expanded form... a number written as the sum of it's parts.

Answers:Standard form is the way you write any number normally. Like writing five thousand and six in stand form would be 5006.

Question:I know standard form is Ax+By=C or something but I dont know the definition or how to find it. Can someone please tell me how to find it and the definition? Also can you please help me with this equation. I need to put the equation of the line with slope 1/2 through (1,-5) into standard form, or y=1/2x-11/2 or something

Answers:y = mx + b is slope-intercept form and you need m and b to write the equation of a line in your case y = -5, x = 1 and m = (1/2) plug them in and solve for b. - 5 = (1/2)(1) + b - 5 = (1/2) + b - 5.5 = b or (-11/2) Now that you have m and b... y = (1/2)x - (11/2) Now you have to change it to Standard Form, which just means moving stuff around. Multiply through by 2 (to get rid of the fractions) 2y = x - 11 Subtract x -x + 2y = -11 Multiply through by -1 (to get rid of the -1x) x - 2y = 11

Question:1- Power of a Power Property 2-Power of a Product Property 3-A Nonzero number to the zero power is 1. Give an example:____ 4-a^-n is the reciprocal of a^n : a^-n = 1/a^n "a" cannot = zero 5-Quotient of Powers Property 6-Power of a Quotient Property 7- Scientific Notation 8-Exponential Growth 9-Exponential Growth Thanks! =D

Answers:Dear,I searched the whole net..but couldn't find any as they are not proper mathematical terms. But I know what a Scientific Notation is. Scientific notation is a mathematical format used to write very large and very small numbers; this system avoids using a lot of zeros by using powers (exponents). Hope this helps!!