Copyright (c) 2010 Pearson Education, Inc. Laws of Exponents

Tobey & Slater, Beginning Algebra, 7e2 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, Beginning Algebra, 7e3 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 c.) 4w 2 · 2w 5 = (4)(2)w = 8w 7

Tobey & Slater, Beginning Algebra, 7e4 The Quotient Rule Example: Divide. The Quotient Rule To divide two exponential expressions that have the same base, keep the base and subtract the exponents.. The Quotient Rule To divide two exponential expressions that have the same base, keep the base and subtract the exponents.. Remember that the base does not change. a.)

Tobey & Slater, Beginning Algebra, 7e5 The Quotient Rule (by cancellation) Example: Divide. a.) b.) Quotient Rule

Tobey & Slater, Beginning Algebra, 7e6 Negative Exponents Negative exponents determine POSITION of the expression. Negative exponents DO NOT change the sign of the expression. Negative Exponent Properties:

Tobey & Slater, Beginning Algebra, 7e7 Zero Power The Zero Power Property:, if x  0 (0 0 remains undefined). The Zero Power Property:, if x  0 (0 0 remains undefined). Example Simplify:

Tobey & Slater, Beginning Algebra, 7e8 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, Beginning Algebra, 7e9 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, Beginning Algebra, 7e10 Quotient Raised to a Power if y  0. Example: Simplify. a.) b.)