A

David

Darling

power (in mathematics)

'Power' is a word that is almost never used in its correct, original sense any more. Strictly speaking, if we write 8 = 23, then 2 is the base, 3 is the exponent, and 8 is the power. But almost everyone, including most mathematicians, would say that 3 is the power, and that ''power' and 'exponent' mean the same thing. The misuse has probably come about from a misunderstanding of statements such "eight is the third power of two."

 

A power is a product of equalfactors. E.g., 43 = 4 × 4 × 4; a5 = a × a × a × a × a. Evaluating the product, we obtain the value of the power, e.g. 43 = 64; 32 = 9; a1 = a.

 

In particular, we have 1n = 1 and 0n = 0 for all values of n.