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Zeroth power

Exponentiation is a mathematical operation, written as $b n$ , 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, $b n$ is the product of multiplying $n$ bases:

The exponent is usually shown as a superscript to the right of the base. In that case, $b n$ is called "b raised to the n-th power", "b raised to the power of n", or "the n-th power of b".

When $n$ is a positive integer and $b$ is not zero, $b - n$ is naturally defined as $1 / b n$ , preserving the property $b n \times b m = b n + m$ . With exponent −1, $b -1$ is equal to $1 / b$ , and is the reciprocal of $b$ .

The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices.

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