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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. The word "raised" is usually omitted, and sometimes "power" as well, so 3 5 can be simply read "3 to the 5th", or "3 to the 5".
In arithmetic and algebra, the eighth power of a number n is the result of multiplying eight instances of n together. So: n 8 = n × n × n × n × n × n × n × n. Eighth powers are also formed by multiplying a number by its seventh power, or the fourth power of a number by itself. The sequence of eighth powers of integers is:
According to Guy, Erdős has asked whether there are infinitely many pairs of consecutive powerful numbers such as (23 3, 2 3 3 2 13 2) in which neither number in the pair is a square. Walker (1976) showed that there are indeed infinitely many such pairs by showing that 3 3 c 2 + 1 = 7 3 d 2 has infinitely many solutions.
y = x 3 for values of 1 ≤ x ≤ 25. 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 n is denoted n 3, using a superscript 3, [a] for example 2 3 = 8. The cube operation can also be defined for any other mathematical expression, for ...
When doing quick estimates, 3 is a rough approximation of π, 3.1415..., and a very rough approximation of e, 2.71828... 3 is the first Mersenne prime , as well as the second Mersenne prime exponent and the second double Mersenne prime exponent , for 7 and 127 , respectively. 3 is also the first of five known Fermat primes , which include 5, 17 ...
The term superexponentiation was published by Bromer in his paper Superexponentiation in 1987. [3] It was used earlier by Ed Nelson in his book Predicative Arithmetic, Princeton University Press, 1986. The term hyperpower [4] is a natural combination of hyper and power, which aptly describes tetration.
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By Mihăilescu's Theorem, it is the only nonzero perfect power that is one less than another perfect power. 8 is the first proper Leyland number of the form x y + y x, where in its case x and y both equal 2. [4] 8 is a Fibonacci number and the only nontrivial Fibonacci number that is a perfect cube. [5] Sphenic numbers always have exactly eight ...