Fourth power - Wikipedia Fourth power This article is about mathematics. For other uses, see Fourth branch of government and Fourth Estate. In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together. So : n = n × n × n × n Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares. The sequence of fourth powers of integers ( also known as biquadratic numbers or tesseractic numbers ) is : 0, 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000, 14641, 20736, 28561, 38416, 50625, 65536, 83521, 104976, 130321, 160000, 194481, 234256, 279841, 331776, 390625, 456976, 531441, 614656, 707281, 810000,... ( sequence A000583 in the OEIS ) Contents 1 Properties 2 Equations containing a fourth power 3 See also 4 References Properties The last two digits of a fourth power of an integer in base 10 can be easily shown ( for instance, by computing the squares of possible last two digits of square numbers ) to be restricted to only twelve possibilities : if a number ends in 0, its fourth power ends in 00 ( displaystyle 00 ) ( in fact in 0000 ( displaystyle 0000 ) ) if a number ends in 1, 3, 7 or 9 its fourth power ends in 01 ( displaystyle 01 ), 21 ( displaystyle 21 ), 41 ( displaystyle 41 ), 61 ( displaystyle 61 ) or 81 ( displaystyle 81 ) if a number ends in 2, 4, 6, or 8 its fourth power ends in 16 ( displaystyle 16 ), 36 ( displaystyle 36 ), 56 ( displaystyle 56 ), 76 ( displaystyle 76 ) or 96 ( displaystyle 96 ) if a number ends in 5 its fourth power ends in 25 ( displaystyle 25 ) ( in fact in 0625 ( displaystyle 0625 ) ) These twelve possibilities can be conveniently expressed as 00, e1, o6 or 25 where o is an odd digit and e an even digit. Every positive integer can be expressed as the sum of at most 19 fourth powers ; every sufficiently large integer can be expressed as the sum of at most 16 fourth powers ( see Waring 's problem ). Fermat knew that a fourth power can not be the sum of two other fourth powers ( the n = 4 case of Fermat 's Last Theorem ; see Fermat 's right triangle theorem ). Euler conjectured that a fourth power can not be written as the sum of three fourth powers, but 200 years later, in 1986, this was disproven by Elkiies with : 20615673 4 = 18796760 4 + 15365639 4 + 2682440 4. ( displaystyle 20615673 ^ ( 4 ) = 18796760 ^ ( 4 ) + 15365639 ^ ( 4 ) + 2682440 ^ ( 4 ). ) Elkies showed that there are infinitely many other counterexamples for exponent four, some of which are : 2813001 4 = 2767624 4 + 1390400 4 + 673865 4 ( displaystyle 2813001 ^ ( 4 ) = 2767624 ^ ( 4 ) + 1390400 ^ ( 4 ) + 673865 ^ ( 4 ) ) ( Allan MacLeod ) 8707481 4 = 8332208 4 + 5507880 4 + 1705575 4 ( displaystyle 8707481 ^ ( 4 ) = 8332208 ^ ( 4 ) + 5507880 ^ ( 4 ) + 1705575 ^ ( 4 ) ) ( D.J. Bernstein ) 12197457 4 = 11289040 4 + 8282543 4 + 5870000 4 ( displaystyle 12197457 ^ ( 4 ) = 11289040 ^ ( 4 ) + 8282543 ^ ( 4 ) + 5870000 ^ ( 4 ) ) ( D.J. Bernstein ) 16003017 4 = 14173720 4 + 12552200 4 + 4479031 4 ( displaystyle 16003017 ^ ( 4 ) = 14173720 ^ ( 4 ) + 12552200 ^ ( 4 ) + 4479031 ^ ( 4 ) ) ( D.J. Bernstein ) 16430513 4 = 16281009 4 + 7028600 4 + 3642840 4 ( displaystyle 16430513 ^ ( 4 ) = 16281009 ^ ( 4 ) + 7028600 ^ ( 4 ) + 3642840 ^ ( 4 ) ) ( D.J. Bernstein ) 422481 4 = 414560 4 + 217519 4 + 95800 4 ( displaystyle 422481 ^ ( 4 ) = 414560 ^ ( 4 ) + 217519 ^ ( 4 ) + 95800 ^ ( 4 ) ) ( Roger Frye, 1988 ) 638523249 4 = 630662624 4 + 275156240 4 + 219076465 4 ( displaystyle 638523249 ^ ( 4 ) = 630662624 ^ ( 4 ) + 275156240 ^ ( 4 ) + 219076465 ^ ( 4 ) ) ( Allan MacLeod, 1998 ) That the equation x + y = z has no solutions in nonzero integers ( a special case of Fermat 's Last Theorem ), was known by Fermat ; see Fermat 's right triangle theorem. Equations containing a fourth power Fourth - degree equations, which contain a fourth degree ( but no higher ) polynomial are, by the Abel -- Ruffini theorem, the highest degree equations having a general solution using radicals. See also Square ( algebra ) Cube ( algebra ) Exponentiation Fifth power ( algebra ) Sixth power Seventh power Perfect power References Jump up ^ Quoted in Meyrignac, Jean - Charles ( 14 February 2001 ). `` Computing Minimal Equal Sums Of Like Powers : Best Known Solutions ''. Retrieved 17 July 2017. Weisstein, Eric W. `` Biquadratic Number ''. MathWorld. Classes of natural numbers Powers and related numbers Achilles Power of 2 Power of 10 Square Cube Fourth power Fifth power Sixth power Seventh power Perfect power Powerful Prime power Of the form a × 2 ± 1 Cullen Double Mersenne Fermat Mersenne Proth Thabit Woodall Other polynomial numbers Carol Hilbert Idoneal Kynea Leyland Lucky numbers of Euler Repunit Recursively defined numbers Fibonacci Jacobsthal Leonardo Lucas Padovan Pell Perrin Possessing a specific set of other numbers Knödel Riesel Sierpinski Expressible via specific sums Nonhypotenuse Polite Practical Primary pseudoperfect Ulam Wolstenholme Generated via a sieve Lucky Code related Meertens Figurate numbers 2 - dimensional centered Centered triangular Centered square Centered pentagonal Centered hexagonal Centered heptagonal Centered octagonal Centered nonagonal Centered decagonal Star non-centered Triangular Square Square triangular Pentagonal Hexagonal Heptagonal Octagonal Nonagonal Decagonal Dodecagonal 3 - dimensional centered Centered tetrahedral Centered cube Centered octahedral Centered dodecahedral Centered icosahedral non-centered Tetrahedral Octahedral Dodecahedral Icosahedral Stella octangula pyramidal Square pyramidal Pentagonal pyramidal Hexagonal pyramidal Heptagonal pyramidal 4 - dimensional centered Centered pentachoric Squared triangular non-centered Pentatope Pseudoprimes Carmichael number Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler -- Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime Lucas pseudoprime Somer -- Lucas pseudoprime Strong pseudoprime Combinatorial numbers Bell Cake Catalan Dedekind Delannoy Euler Fuss -- Catalan Lazy caterer 's sequence Lobb Motzkin Narayana Ordered Bell Schröder Schröder -- Hipparchus Arithmetic functions By properties of σ ( n ) Abundant Almost perfect Arithmetic Colossally abundant Descartes Hemiperfect Highly abundant Highly composite Hyperperfect Multiply perfect Perfect Practical number Primitive abundant Quasiperfect Refactorable Sublime Superabundant Superior highly composite Superperfect By properties of Ω ( n ) Almost prime Semiprime By properties of φ ( n ) Highly cototient Highly totient Noncototient Nontotient Perfect totient Sparsely totient By properties of s ( n ) Amicable Betrothed Deficient Semiperfect Euclid Fortunate Dividing a quotient Wieferich Wall -- Sun -- Sun Wolstenholme prime Wilson Other prime factor or divisor related numbers Blum Erdős -- Nicolas Erdős -- Woods Friendly Frugal Giuga Harmonic divisor Lucas -- Carmichael Pronic Regular Rough Smooth Sociable Sphenic Størmer Super-Poulet Zeisel Recreational mathematics Base - dependent numbers Automorphic Cyclic Digit - reassembly Dudeney Equidigital Extravagant Factorion Friedman Happy Harshad Kaprekar Keith Lychrel Missing - digit sum Narcissistic Palindromic Pandigital Parasitic Pernicious Polydivisible Primeval Repdigit Repunit Self Self - descriptive Smarandache -- Wellin Strictly non-palindromic Strobogrammatic Sum - product Transposable Trimorphic Undulating Vampire Aronson 's sequence Ban Pancake number This algebra - related article is a stub. You can help Wikipedia by expanding it. Retrieved from `` https://en.wikipedia.org/w/index.php?title=Fourth_power&oldid=827431528 '' Categories : Integers Number theory Elementary arithmetic Integer sequences Unary operations Algebra stubs Talk Contents About Wikipedia 한국어 日本 語 Svenska தமிழ் 中文 Edit links This page was last edited on 24 February 2018, at 18 : 18. Text is available under the Creative Commons Attribution - ShareAlike License ; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia ® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. About Wikipedia

Question: how to say to the power of 4
Answer: fourth power