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ELF.01.1 - Reviewing Exponent Laws

ELF.01.1 - Reviewing Exponent Laws. MCB4U - Santowski. (A) Review of Exponent Laws. product of powers: 3 4 x 3 6 3 4 x 3 6 = 3 4 + 6  add exponents if bases are equal quotient of powers: 3 9 ÷ 3 2 6 9 ÷ 6 2 = 6 9 - 2  subtract exponents if bases are equal

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ELF.01.1 - Reviewing Exponent Laws

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  1. ELF.01.1 - Reviewing Exponent Laws MCB4U - Santowski

  2. (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

  3. (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

  4. (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.

  5. (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

  6. (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 .....

  7. (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)

  8. (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

  9. (G) Internet Links • From West Texas A&M - Integral Exponents • From West Texas A&M - Rational Exponents

  10. (H) Homework • Nelson textbook, p84 • Q1-10, 13,16,17

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