These rules for exponents
give some insight into why
logarithms are useful for performing multiplication, division, and
The exponent is usually shown as a superscript to the right of the base. The
exponentiation an can be read as: a raised to the n-th power, a raised to the power [of] n or possibly
a raised to the exponent [of] n, or more briefly: a to the n-th power or a to the power [of] n, or even more
briefly: a to the n. Some exponents have their own pronunciation: for example, a2 is usually read as a
squared and a3 as a cubed.
The power an can be defined also when n is a negative integer, at
least for nonzero a. No natural extension to all real a and n exists, but when the base a is a positive real
number, an can be defined for all real and even complex exponents n via the exponential function ez.
Trigonometric functions can be expressed in terms of complex exponentiation.