Algebraic properties of exponentials (“the laws of exponents”)

e^{x+y} = e^{x}e^{y}

(e^{x})^{y} = e^{xy}

e^{−x} = \frac{1}{e^{x}}

(ab)^{x} = a^{x}b^{x}

e^{x} ≥ 0

e^{0} = 1

e^{1} = e; a^{1} = a

Except as noted in the last line, these laws also hold for a^{x}.