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When an exponent is a positive integer, that exponent indicates how many copies of the base are multiplied together. For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243. The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3, or 3 raised to the 5th power.
Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. Some variants are commonly referred to as square-and-multiply algorithms or binary exponentiation.
The multiplication of two complex numbers can be expressed most easily in polar coordinates — the magnitude or modulus of the product is the product of the two absolute values, or moduli, and the angle or argument of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as ...
When multiplication is repeated, the resulting operation is known as exponentiation. For instance, the product of three factors of two (2×2×2) is "two raised to the third power", and is denoted by 2 3, a two with a superscript three. In this example, the number two is the base, and three is the exponent. [26]
A cell on a different sheet of the same spreadsheet is usually addressed as: =SHEET2!A1 (that is; the first cell in sheet 2 of the same spreadsheet). Some spreadsheet implementations in Excel allow cell references to another spreadsheet (not the currently open and active file) on the same computer or a local network.
In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together. So: n 4 = n × n × n × n. Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares.
The sum of powers of two from zero up to a given positive integer power is 1 less than the next power of two (i.e. the next Mersenne number). The simple, brute-force solution is just to manually double and add each step of the series:
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