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
Algebra 1 Section 1.7 Definition For x N, bx is the product of x factors of b. The repeated factor, b, is the When numbers are written this base. way, they are said to be in The exponent [x] indicates exponential form or how many times bnotation. is used as a exponential factor. Exponents 63 = 6 × 6 × 6 “6 to the third power” “6 cubed” 6 6 6 Exponents 52 = 5 × 5 “5 to the second power” “5 squared” 5 5 Example 1 a. 2 • 2 • 2 • 2 • 2 • 2 • 2 = 27 b. -3 • (-3) • (-3) • (-3) = (-3)4 An Important Distinction -34 = -1 • 34 = -81 (-3)4 = -3 • (-3) • (-3) • (-3) = 81 Example 2 Evaluate: a. 93 = 9 • 9 • 9 = 729 b. (-7)4 = -7 • (-7) • (-7) • (-7) = 2401 c. -42 = -(4 • 4) = -16 Properties of Exponents 52 • 53 52+3 85 ÷ 82 8•8•8•8•8 8•8 55 85-2 (5 • 5)(5 • 5 • 5) 83 Properties of Exponents Product Property: To multiply like bases, add the exponents. xa • xb = xa+b Properties of Exponents Quotient Property: To divide like bases, subtract the exponents. xa a-b for x 0 = x xb Properties of Exponents Power Property: To raise a power to a power, multiply the exponents. (xa)b = xab Example 3 Leave in exponential form: a. 52 • 510 = 52+10 = 512 b. 32 • 34 • 39 = 32+4+9 = 315 c. 24 ÷ 2 = 24-1 = 23 d. 105 ÷ 103 = 105-3 = 102 e. (53)6 = 53(6) = 518 Properties of Exponents The Quotient Property allows us to give meaning to negative exponents. x2 2-3 = x-1 = x x3 x2 1 = x3 x1 Properties of Exponents Any nonzero number to the zero power equals 1. When x 0, x0 = 1 Properties of Exponents Negative exponents: x-a 1 = a x 1 a = x x-a Example 4 Evaluate. 1 1 = a. (-2)-4 = (-2)4 16 1 1 b. -3-2 = - 2 = 9 3 1 c. -3 = 63 = 216 6 Example 5 Simplify, leaving each answer in positive exponential form: 1 a. 3-9 • 37 = 3-9+7 = 3-2 = 2 3 1 b. 2-3 • 2-2 = 2-3+(-2) = 2-5 = 5 2 Example 5 Simplify, leaving each answer in positive exponential form: c. 4-2 ÷ 4-3 = 4-2-(-3) = 41 = 4 1 d. (5-3)4 = 5-3(4) = 5-12 = 12 5 Homework: pp. 36-37