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 e^z. Trigonometric functions can be expressed in terms of complex exponentiation. - Wikipedia

a^x · a^y = a ^(x+y)
( a · b )^x = a^x · b^x
( a^x )^y = a ^x·y

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