Laws

• exponentiation is right-distributive over multiplication (m n) ↑ x = m ↑ x n ↑ x

• exponentiation is not left-distributive over multiplication x ↑ (m n) = (x ↑ m) (x ↑ n)

xⁿ = x xⁿ⁻¹ xᵐ xⁿ = xᵐᐩⁿ (xᵐ)ⁿ = (xⁿ)ᵐ = xⁿᵐ

• exponentiation is not associative

  (x ↑ m) ↑ n = (xᵐ)ⁿ

  (x ↑ m) ↑ n ≠ x ↑ (m ↑ n)

• log: natural logarithm

  exp (log x) = x = log (exp x)

  √x = exp(1/2 log x)

exp x = lim (1 + x/n)ⁿ x->∞