Lesson Intermediate Algebra Formulas Review

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 ALGEBRAIC PROPERTIES Commutative Property: {{{a + b = b + a}}}(for addition) {{{ab = ba}}} (for multiplication) Associative Property: {{{(a + b) + c = a + (b + c)}}}(for addition) {{{(ab)*c = a*(bc)}}}(for multiplication) Distributive Property of Multiplication Over Addition: {{{a*(b + c) = ab + ac}}} {{{(b + c)*a = ba + ca}}} Identity Property: {{{a + 0 = a}}}(for addition) {{{a*1 = a}}}(for multiplication) PROPERTIES OF EXPONENTS Product of Powers {{{a^m*a^n=a^(m+n)}}} Power of Power {{{(a^m)^n=a^(mn)}}} Power of a Product {{{(ab)^m=a^m*b^m}}} Negative Exponent {{{a^(-m)=1/(a^m)}}} where {{{a<>0}}} Zero Exponent {{{a^0=1}}} where {{{a<>0}}} Quotient of Powers {{{(a^m)/(a^n)=a^(m-n)}}} where {{{a<>0}}} Powers of a Quotient {{{(a/b)^m=(a^m)/(b^m)}}} where {{{b<>0}}} SLOPES AND INTERCEPTS If a line passes through points (x1,y1) and (x2,y2) the the slope m is {{{m=(y2-y1)/(x2-x1)}}} If a line passes through a point (x1,y1) with a slope m then the equation for that line is {{{y-y1=m(x-x1)}}} (point-slope form) If an equation for a line is in a slope-intercept form {{{y=mx+b}}} then the ordered pair (0,b) is the y-intercept If an equation for a line is in the form {{{x=(1/m)y+c}}} then the ordered pair (c,0) is the x-intercept