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Key Equations

Key Equations

Rules of Exponents
 For nonzero real numbers a a and b b and integers m m and n n
Product rule a m ⋅ a n = a m+n a m ⋅ a n = a m+n
Quotient rule a m a n = a m−n a m a n = a m−n
Power rule ( a m ) n = a m⋅n ( a m ) n = a m⋅n
Zero exponent rule a 0 =1 a 0 =1
Negative rule a −n = 1 a n a −n = 1 a n
Power of a product rule ( a⋅b ) n = a n ⋅ b n ( a⋅b ) n = a n ⋅ b n
Power of a quotient rule ( a b ) n = a n b n ( a b ) n = a n b n
perfect square trinomial (x+a) 2 =(x+a)(x+a)= x 2 +2ax+ a 2 (x+a) 2 =(x+a)(x+a)= x 2 +2ax+ a 2
difference of squares (a+b)(a−b)= a 2 − b 2 (a+b)(a−b)= a 2 − b 2
difference of squares a 2 − b 2 =(a+b)(a−b) a 2 − b 2 =(a+b)(a−b)
perfect square trinomial a 2 +2ab+ b 2 = (a+b) 2 a 2 +2ab+ b 2 = (a+b) 2
sum of cubes a 3 + b 3 =(a+b)( a 2 −ab+ b 2 ) a 3 + b 3 =(a+b)( a 2 −ab+ b 2 )
difference of cubes a 3 − b 3 =(a−b)( a 2 +ab+ b 2 ) a 3 − b 3 =(a−b)( a 2 +ab+ b 2 )