Untitled Flashcard Set

Commutative Property

a+b = b+a and ab = ba,

Associative Property

(a+b)+c = a+(b+c) and (ab)c = a(bc),

Distributive Property

a(b+c) = ab + ac

Identity Property

a+0 = a and a⋅1 = a

Inverse Property

a+(-a) = 0 and a⋅(1/a) = 1 for a ≠ 0,

Addition Property of Equality

a=b, then a+c=b+c,

Multiplication Property of Equality

a=b, then ac=bc,

Product Rule (Exponents)

x^m ⋅ x^n = x^{m+n},

Quotient Rule (Exponents)

x^m/x^n = x^{m-n}.

Power Rule (Exponents)

(x^m)^n = x^{mn}

Power of a Product Rule (Exponents)

(ab)^n = a^n b^n

Power of a Quotient Rule (Exponents)

(a/b)^n = a^n/b^n

Zero Exponent Rule

a^0 = 1 for a ≠ 0

Negative Exponent Rule

a^{-n} = 1/a^n

Fractional Exponent Rule

States that a^{m/n} =
oot[n]{a^m} = (
oot[n]{a})^m, linking exponents with roots.

Definition of a Logarithm

log_a(b) = c if and only if a^c = b,

Log Product Rule

loga(MN) = loga(M) + log_a(N)

Log Quotient Rule

loga(M/N) = loga(M) - log_a(N)

Log Power Rule

loga(M^k) = k⋅loga(M)

Change of Base Formula

loga(M) = logb(M)/log_b(a)

Special Log Values / Identity

loga(a) = 1 and loga(1) = 0