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8.2 Dividing Monomials Begin 2 column notes… Algebra 1 Glencoe Mathematics 8-2 Dividing Monomials pages 417-423 What You’ll Learn •Simplify expressions involving the quotient of monomials •Simplify expressions containing negative exponents How How can you compare pH levels? table on page 417 c = concentration of hydrogen ions æ1 öpH c = ççç ÷ ÷ çè10 ÷ ÷ ø Continue 2 column notes… Vocabulary Quotients of Monomials zero exponent ; negative exponent Key Concept Words Quotient of Powers Symbols Why can’t a be zero? To divide two powers that have the same base, subtract the exponents. For all integers m and n and any nonzero number a, am an Example b15 b7 = am- n = b15- 7 or b8 Stop: Let’s look at Example 1 Simplify 5 8 a b 3 ab = a5b8 ab3 a5b8 a1b3 = a5- 1b8- 3 = a 4b5 a m n a = a m- n Stop: Let’s learn the Miller method Simplify a5b8 ab3 = a5b8 ab3 a 4b5 aaaaabbbbbbbb ( ) abbb Continue 2 column notes… Key Concept Words Power of a Quotient To find the power of a quotient, find the power of the numerator and the power of the denominator. Symbols For any integer m and any real numbers a and m æ ö b, b≠0 ç a ÷ am = çç ÷ ÷ çèb ÷ ø bm Example æc ö5 c5 çç ÷ = ççè d ÷ ÷ ÷ ø d5 Stop: Let’s look at Example 2: 4 æ2p2 ö ÷ Simplify ç çç ÷ ççè 3 ÷ ÷ ÷ ø 4 æ2p2 ö çç ÷ ÷ çç ÷ çè 3 ÷ ÷ ø 4 2×4 = 2 p 4 3 8 16p = 81 Continue 2 column notes… Negative Exponents Study Tip p418 How do you change a decimal to a fraction with the graphing calculator? Study Tip p419 See Miller Method for example 1 To change a number to a fraction press MATH ENTER ENTER Continue 2 column notes… Key Concept Zero Exponent Words Symbols Example Any nonzero number raised to the zero power is 1. a0 = 1 (-0.25)0 = 1 STOP. Let’s look at Example 3: Simplify 0 5 ö A) æ ç 3x y ÷ çç ÷ = 1 ÷ ççè8xy 7 ÷ ÷ ø B) 3 t (1) t s = = t t 3 0 t3 = t t2 Continue 2 column notes… Key Concept Negative Exponent Words For any nonzero number a and any integer n, a-n is the reciprocal of an. In addition, the reciprocal of a-n is an. Symbols For any nonzero number a and any integer n, - n a Example 5- 2 = = 1 an 1 2 5 and or 1 25 1 a- n 1 m- 3 = an = m3 Stop. Lets look at Example 4: (the Miller method) Simplify - 3 2 A) b c - 5 d 2 5 Negative exponents = c d 3 b - 4 7 - 3a B) b 2 7 - 5 21a b c change to other side of fraction bar -1 7 5 = = - 3b c 2 4 7 21a a b 5 - c 7a 6 = 7 5 - 3b c 6 7 21a b 7 SKIP Example 5 Homework p421 15-37odd