# Rules of Exponents

These rules for exponents give some insight into why logarithms are useful for performing multiplication, division, and exponent operations.

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. - Wikipedia

 ax · ay = a (x+y) ( a · b )x = ax · bx ( ax )y = a x·y