Exponentiation

Graphs of y = bx for various bases b: base 10 (green), base e (red), base 2 (blue), and base 1/2 (cyan). 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.

From top to bottom: x1/8, x1/4, x1/2, x1, x2, x4, x8.

The exponential function ez can be defined as the limit of (1 + z/N)N, as N approaches infinity, and thus eiπ is the limit of (1 + iπ/N)N. In this animation N takes values increasing from 1 to 100. The computation of (1 + iπ/N)N is displayed as the combined effect of N repeated multiplications in the complex plane, so that (1 + iπ/N)k, k = 0 ... N are the vertices of a polygonal path whose final, leftmost endpoint is the actual value of (1 + iπ/N)N. It can be seen that as N gets larger (1 + iπ/N)N approaches a limit of −1. Therefore, eiπ = −1, which is known as Euler's identity.

Exponentiation is a mathematical operation, written as b, involving two numbers, the base b and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b is the product of multiplying n bases:

单词	Raising to a power
释义	Raising to a power 英语百科 Exponentiation Exponentiation is a mathematical operation, written as b, involving two numbers, the base b and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b is the product of multiplying n bases:
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Raising to a power

Exponentiation