Algebra and Trigonometry presents a finished and multi-layered exploration of algebraic rules. The textual content is acceptable for a customary introductory Algebra & Trigonometry direction, and used to be constructed for use flexibly. The modular strategy and the richness of content material guarantees that the publication meets the desires of numerous courses. Algebra and Trigonometry publications and helps scholars with differing degrees of instruction and event with arithmetic. rules are offered as in actual fact as attainable, and growth to extra complicated understandings with massive reinforcement alongside the best way. A wealth of examples - often numerous dozen in step with bankruptcy - supply distinct, conceptual reasons, so one can construct in scholars a powerful, cumulative origin within the fabric sooner than asking them to use what they have discovered. this can be a full-color textbook.
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For instance, consider (pq)3. We begin by using the associative and commutative properties of multiplication to regroup the factors. 3 factors (pq)3 = (pq) · (pq) · (pq) =p·q·p·q·p·q =p·p·p·q·q·q = p3 · q3 3 factors 3 factors In other words, (pq)3 = p3 · q3. the power of a product rule of exponents For any nonzero real number a and natural number n, the negative rule of exponents states that (ab)n = an bn Example 7 Using the Power of a Product Rule Simplify each of the following products as much as possible using the power of a product rule.
04 × 1013) d. 6 × 105) e. 62 × 105) Solution a. 291 × 104 Scientific notation 4 105 ___ 9 b. 63 × 10−4 Scientific notation c. 2 108 ___ d. 25 × 102 Scientific notation e. 965 × 1017 27 28 CHAPTER 1 Prerequisites Try It #12 Perform the operations and write the answer in scientific notation. 81 × 102) Example 13 Applying Scientific Notation to Solve Problems In April 2014, the population of the United States was about 308,000,000 people. The national debt was about $17,547,000,000,000.
2 Exponents and Scientific Notation Try It #7 Simplify each of the following products as much as possible using the power of a product rule. Write answers with positive exponents. _______ 6 7 3 (a b ) Finding the Power of a Quotient To simplify the power of a quotient of two expressions, we can use the power of a quotient rule, which states that the power of a quotient of factors is the quotient of the powers of the factors. For example, let’s look at the following example. f 14 (e −2f 2)7 = _ e14 Let’s rewrite the original problem differently and look at the result.