1, 1, 4, 27, 256,… ...what's the next number?

The sequence consists of numbers of the form x^x ("^" means "raised to the power of"). So we have 0^0=1, 1^1=1, 2^2=4, 3^3=27, 4^4=256 (or, equivalently, four times four times four times four). So the next number is 5^5 (five times five times five times five times five) which works out as 3125.

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66 Comments

Ike Hinlo Caceres

The first 1 is not needed.

timwhitestevens

Steve Edwards, I agree.

timwhitestevens

Actually, 0^0 is undefined. The limit as x approaches 0 of x^x = 1

Steve Edwards

0^0 is undefined - it is not equal to 1. For those saying that any number to the power of 0 always equals 1, you could also say that 0 to the power of any number always equals 0. Wikipedia has this to say on the subject: “Zero to the power of zero, denoted by 00, is a mathematical expression with no agreed-upon value. The most common possibilities are 1 or leaving the expression undefined, with justifications existing for each, depending on context. In algebra, combinatorics, or set theory, the generally agreed upon value is 00 = 1, whereas in mathematical analysis, the expression is generally left undefined. Computer programs also have differing ways of handling this expression.”