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In arithmetic and algebra, the fifth power or sursolid [1] of a number n is the result of multiplying five instances of n together: n 5 = n × n × n × n × n. Fifth powers are also formed by multiplying a number by its fourth power, or the square of a number by its cube. The sequence of fifth powers of integers is:
Graphs of y = b x for various bases b: base 10, base e, base 2, base 1 / 2 . Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.
In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2 3 = 8 or (x + 1) 3. The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n.
In the third expression, n is the height, but each of the bases is different. Care must be taken when referring to iterated exponentials, as it is common to call expressions of this form iterated exponentiation, which is ambiguous, as this can either mean iterated powers or iterated exponentials .
Let the right triangle have sides (u, v, w), where the area equals uv / 2 and, by the Pythagorean theorem, u 2 + v 2 = w 2. If the area were equal to the square of an integer s uv / 2 = s 2. then by algebraic manipulations it would also be the case that 2uv = 4s 2 and −2uv = −4s 2. Adding u 2 + v 2 = w 2 to these equations gives
In arithmetic and algebra the sixth power of a number n is the result of multiplying six instances of n together. So: n 6 = n × n × n × n × n × n. Sixth powers can be formed by multiplying a number by its fifth power, multiplying the square of a number by its fourth power, by cubing a square, or by squaring a cube. The sequence of sixth ...
In this system the perfect fifth is flattened by one quarter of a syntonic comma ( 81 : 80 ), with respect to its just intonation used in Pythagorean tuning (frequency ratio 3 : 2 ); the result is 3 / 2 × [ 80 / 81 ] 1 / 4 = 4 √ 5 ≈ 1.49535, or a fifth of 696.578 cents. (The 12th power of that value is 125, whereas 7 octaves ...
Perfect fifth (3/2), a musical interval "1.5" (song), a 2018 song by 21 Savage This page was last edited on 21 July ...