# Exponent calculator

In mathematics, the term "exponentiation" is widely used, that is, multiplying a number by itself. The second power is a single multiplication, the third power is a double multiplication. If the number is denoted by the letter a, the degree by the letter n, then the expression will look like a^n. In this case, a will be called the base of the degree, and n - the exponent.

## A bit of history

The definitions “number squared” and “number cubed”, which are familiar to us, arose in ancient Greece. Then they were called a little differently: “square on segment a” and “cube on a”. Greek mathematicians did not use higher degrees (above the third), and the need for them arose only during the Late Middle Ages and the New Age: as a component of scientific and technological progress.

Until the 17th century in Europe, the degree of numbers was written with letter symbols. So, the symbol q meant a square, c - a cube, qq - a bi-square, and so on. Another common form of writing was the lowercase listing of factors, for example - xx or xxx, which equaled x squared and cubed, respectively.

The French scientist Pierre Erigon and the Scottish mathematician James Hume proposed their own system - to write the degree lowercase, to the right of the base. That is, write modern a² and a³ as a2 and a3.

Experiments with displaying degrees continued until 1637, when the French scientist René Descartes introduced the now convenient form: a^n. At the same time, the indicator n until the 70s of the 17th century could be expressed by any natural numbers, except for two (square). And the square of the number continued to be written as a2.

In 1676, Isaac Newton and John Valles extended the system proposed by Descartes to include fractional and negative exponents. In 1679, numbers began to be raised to a variable degree (at the suggestion of Gottfried Leibniz), and in 1743 - to an imaginary one (at the initiative of Leonhard Euler)).

## Modern definition

Today, the definition of degrees is clearly articulated and expressed in formulas that have stood the test of time and have not changed over the past 200-250 years. According to official mathematical reference books, the power n of a number a is the product of factors of magnitude a n times in a row. Or, if we represent this description as a formula, then:

a^n = (a ⋅ a ⋅ a ⋅ ... a),

where the number of factors a after the equal sign is equal to n.

For all degrees, except for the second and third, only "nominal" names are provided: fourth, fifth, twenty-sixth, hundredth, and so on. And the second and third are also called "square" and "cube" respectively.

There is also the concept of "extensions" for powers, which include integer, rational, real, and complex powers. They are included in the sections of higher mathematics, are quite difficult to understand and are used only in complex technical calculations.

## Use in computer science

With the development of digital technologies, it became necessary to use degrees in programming languages for which there is no “two-story” display of characters in the form of a². It was replaced by "one-story" expressions: "**" and "↑". The former was used in Fortran and the latter in Algol.

The final and most common form (for the BASIC programming language and later) was the circumflex symbol "^", which today is used to display degrees not only in programming, but also when writing mathematical formulas on paper (and in text editors) . Using this symbol, the usual expression a² looks like a^2. It is also used in many models of calculators, including engineering ones.

Summing up, we can say that exponentiation is a convenient and indispensable mathematical operation, on which many formulas and physical laws are based. Its inverse operation is extracting the root.

Squaring small numbers can be done in your head, but for more complex calculations, you need either an engineering calculator or an online application with advanced features.