© 2010 Pearson Prentice Hall. All rights reserved Exponents and Polynomials Chapter 5

© 2010 Pearson Prentice Hall. All rights reserved § 5.1 The Rules of Exponents

Tobey, Slater, & Blair, Beginning and Intermediate Algebra, 3e3 An exponent is a “shorthand” number that saves writing the multiplication of the same numbers. exponent 3434 base This is read “three to the fourth power.” Exponents

Tobey, Slater, & Blair, Beginning and Intermediate Algebra, 3e4 The Product Rule Example: Multiply. The Product Rule To multiply two exponential expressions that have the same base, keep the base and add the exponents. x a · x b = x a + b The Product Rule To multiply two exponential expressions that have the same base, keep the base and add the exponents. x a · x b = x a + b a.) c 4 · c 5 = c = c 9 b.) 3a 3 · a 6 = 3a = 3a 9 Numerical coefficient c.) 4w 2 · 2w 5 = (4)(2)w = 8w 7

Tobey, Slater, & Blair, Beginning and Intermediate Algebra, 3e5 The Quotient Rule Example: Divide. The Quotient Rule (Part 1) Use this form if the larger exponent is in the numerator and x  0. The Quotient Rule (Part 1) Use this form if the larger exponent is in the numerator and x  0. Remember that the base does not change. a.) b.)

Tobey, Slater, & Blair, Beginning and Intermediate Algebra, 3e6 The Quotient Rule Example: Divide. The Quotient Rule (Part 2) Use this form if the larger exponent is in the denominator and x  0. The Quotient Rule (Part 2) Use this form if the larger exponent is in the denominator and x  0. Remember that the base does not change. a.) b.)

Tobey, Slater, & Blair, Beginning and Intermediate Algebra, 3e7 The Quotient Rule Example: Divide. The Quotient Rule (Part 3) if x  0 (0 0 remains undefined). The Quotient Rule (Part 3) if x  0 (0 0 remains undefined). a.) b.)

Tobey, Slater, & Blair, Beginning and Intermediate Algebra, 3e8 Raising a Power to a Power To raise a power to a power, keep the same base and multiply the exponents. Raising a Power to a Power To raise a power to a power, keep the same base and multiply the exponents. Raising Exponential Expressions to a Power Example: Simplify. a.) (x 5 ) 3 b.) (y 3 ) 3 = x 5·3 = x 15 = y 3·3 = y 9

Tobey, Slater, & Blair, Beginning and Intermediate Algebra, 3e9 Product Raised to a Power c.) (4x 3 y 2 ) 3 Example: Simplify. a.) (2c) 3 b.) (  5xy) 2 = 4 3 x 9 y 6 = 64x 9 y 6 = (2) 3 c 3 = 8c 3 = (  5) 2 (xy) 2 = 25x 2 y 2

Tobey, Slater, & Blair, Beginning and Intermediate Algebra, 3e10 Quotient Raised to a Power if y  0. Example: Simplify. a.) b.)