Because aⁿ / aⁿ = a⁰ must equal 1 for any nonzero a.

Exponent Rules

The laws for multiplying, dividing and raising powers.

a^{m} a^{n} = a^{m + n},; \frac{a ^{m}}{a ^{n}} = a^{m - n},; (a^{m})^{n} = a^{mn},; a^{- n} = \frac{1}{a ^{n}}

Variables

Each rule follows from the definition of a power as repeated multiplication. Also: $a^{0} = 1$ and $a^{1/ n} = n a$ .

$\frac{2 ^{5} \cdot 2 ^{3}}{2 ^{4}} = 2^{5 + 3 - 4} = 2^{4} = 16$ .

Raise any number to any power, including negative and fractional exponents, with explanations.

Logarithm Rules

Product, quotient, power and change-of-base rules for logarithms.