algebra

fractions

[a/b] + [c/b] gives [(a+c)/b]

multiplying [a/b] by [c/d] gives [ac/bd]

addition and multiplication

∑ca_i = c ∑a_i where c is a constant (distributivity)

∑(a_i ± b_i) = ∑a_i ± ∑b_i (sum and difference rule)

∑_i ∑_j a_i b_j = ∑_j ∑_i a_i b_j(swapping the order of finite summation)

exponents

a^m * aⁿ is equal to a^m+n (where m and n are integers)

(ab)^m is equal to a^m * b^m (where m is an integer)

(a^m)ⁿ is equal to a^m*n (where m and n are integers)

(a/b)^m is equal to (a^m)/(b^m) (where m is an integer)

x⁰ = 1

x^-n is equal to 1/(xⁿ)

(a^m)÷(aⁿ) is equal to (a^m-n) (where m and n are integers)

^m√a is equal to a^1/m

^m√(ab) is equal to (^m√a) * (^m√b)

ⁿ√(a^q) is equal to (ⁿ√a)^q

logarithms

power rule

change of base

product and quotient rule

quadratic equation

quadratic formula