Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
ELF.01.1 - Reviewing Exponent Laws MCB4U - Santowski 1 (A) Review of Exponent Laws product of powers: 34 x 36 34 x 36 = 34 + 6 add exponents if bases are equal quotient of powers: 39 ÷ 32 69 ÷ 62 = 69 - 2 subtract exponents if bases are equal power of a power: (32)4 (32)4 = 32 x 4 multiply powers power of a product: (3 x a)5 (3 x a)5 = 35 x a5 = 243a5 distribute the exponent power of a quotient: (a/3)5 (a/3)5 = a5 ÷ 35 = a5/243 distribute the exponent 2 (B) Review of Zero & Negative Exponent Evaluate 25 ÷ 25. (i) 25 ÷ 25 = 25 – 5 = 20 OR (ii) 25 ÷ 25 = 32 ÷ 32 = 1 Conclusion is that 20 = 1. In general then b0 = 1 Evaluate 23 ÷ 27. (i) 23 ÷ 27 = 23 – 7 = 2-4 OR (ii) 23 ÷ 27 = 8 ÷ 128 = 1/16 = 1/24 Conclusion is that 2-4 = 1/16 = 1/24 In general then b-e = 1/be 3 (C) Review of Rational Exponent We will use the Law of Exponents to prove that 9½ = %9. 9½ x 9½ = 9(½ + ½) = 91 Therefore, 9½ is the positive number which when multiplied by itself gives 9 The only number with this property is 3, or % 9 So what does it mean? It means we are finding the second root of 9 We can go through the same process to develop a meaning to 271/3 271/3 x 271/3 x 271/3 = 27(1/3 + 1/3 + 1/3) = 271 Therefore, 271/3 is the positive number which when multiplied by itself three times gives 27 The only number with this property is 3, or 3 % 3 or the third root of 27 In general, b1/n = n/ b, or that we are finding the nth root of b. 4 (D) The Rational Exponent m/n We can use our knowledge of Laws of Exponents to help us solve bm/n ex. Rewrite 323/5 making use of the Power of powers >>> (321/5)3 so it means we are looking for the 5th root of 32 which is 2 and then we cube it which is 8 In general, bm/n = (n /b)m 5 (E) Important Numbers to Know The numbers 1,4,9,16,25,36,49,64,81,100,121,144 are important because ... Likewise, the numbers 1,8,27,64,125,216,343,512,729 are important because .... As well, the numbers 1,16,81,256, 625 are important because ..... 6 (F) Examples ex 1. Simplify the following expressions: (i) (3a2b)(-2a3b2) (ii) (2m3)4 (iii) (-4p3q2)3 ex 2. Simplify (6x5y3/8y4)2 ex 3. Simplify (-6x-2y)(-9x-5y-2) / (3x2y-4) and express answer with positive exponents ex 4. Evaluate the following (i) (3/4)-2 (ii) (-6)0 / (2-3) (iii) (2-4 + 2-6) / (2-3) 7 (F) Examples We will use the various laws of exponents to simplify expressions. ex. 271/3 ex. (-320.4) ex. 81-3/4 ex. Evaluate 491.5 + 64-1/4 - 27-2/3 ex. Evaluate 41/2 + (-8)-1/3 - 274/3 ex. Evaluate 3/8 + 4/16 - (125)-4/3 ex. Evaluate (4/9)½ + (4/25)3/2 8 (G) Internet Links From West Texas A&M - Integral Exponents From West Texas A&M - Rational Exponents 9 (H) Homework Nelson textbook, p84 Q1-10, 13,16,17 10