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Rules of Exponents. Rules of Exponents. Exponents: The exponent is an abbreviated form of multiplication. x n means “n factors of x”. YTI#1 : State the meaning, write in expanded form and then evaluate. a) 4 3 means b) (-12) 2 means c) 1 6 means. Rules of Exponents.
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Rules of Exponents Exponents: The exponent is an abbreviated form of multiplication xn means “n factors of x” YTI#1: State the meaning, write in expanded form and then evaluate. a) 43 means b) (-12)2 means c) 16 means
Rules of Exponents The first power rule For any base, x1 = x • Recall: Prime Factorization • a) 24 = 2 · 2 · 2 · 3 = • b) 40 = 2 · 2 · 2 · 5 = YTI#2: Evaluate. a) (-2)1 = b) p1 = c) 6 =
Rules of Exponents • The Product Rule: YTI#3: Rewrite in expanded form, then combine all factors using exponential form. a) x5 ·x4 = c) k1 · k1= d) m · m3 =
Rules of Exponents The Product Rule For any nonzero base, xa · xb= xa+b YTI#4: Use the product rule to evaluate each of the following. a) x3 ·x6 = c) k · k4= d) p · p =
Rules of Exponents The Zero Power Rule For any nonzero base, x0 = 1 x≠0 , x0 means “no factors of x” Note: Use the product rule to evaluate x7 ·x0 YTI#5: Use the zero product rule to evaluate each of the following. a) w0 = b) 10= c) (-4)0 = d) p0=
Rules of Exponents The Power Rule for Exponents For any nonzero base, (xa)b = xa·b Note: Evaluate: (x5)3 YTI#7: Simplify each of the following. a) (c6)2 = b) (y2)4= c) (d5)1 = d) (q2)0=
Rules of Exponents Rules of Exponents The first power rule For any base, x1 = x The Zero Power Rule For any nonzero base, x0 = 1 x≠0 , x0 means “no factors of x” The Product Rule For any nonzero base, xa · xb= xa+b The Power Rule for Exponents For any nonzero base, (xa)b = xa·b
