Algebra and Trigonometry by OpenStax

By OpenStax

Algebra and Trigonometry offers a entire and multi-layered exploration of algebraic ideas. The textual content is acceptable for a regular introductory Algebra & Trigonometry path, and was once built for use flexibly. The modular procedure and the richness of content material guarantees that the ebook meets the wishes of quite a few courses. Algebra and Trigonometry courses and helps scholars with differing degrees of practise and event with arithmetic. rules are offered as in actual fact as attainable, and growth to extra advanced understandings with enormous reinforcement alongside the best way. A wealth of examples - frequently a number of dozen in keeping with bankruptcy - provide particular, conceptual causes, so that it will construct in scholars a powerful, cumulative origin within the fabric sooner than asking them to use what they have discovered. it is a full-color textbook.

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B 2 ∙ b−8 = b 2 − 8 = b −6 = ​ __6 ​ b b. (−x)5 ∙ (−x)−5 = (−x)5 − 5 = (−x)0 = 1 (−7z)1 −7z 1 c. ​ _5 ​ = ​ _ ​ = (−7z)1 − 5 = (−7z)−4 = ​ _ ​ (−7z) (−7z)5 (−7z)4 Try It #6 Write each of the following products with a single base. Do not simplify further. Write answers with positive exponents. 2512 a.  ​ ____ ​ 2513 Finding the Power of a Product To simplify the power of a product of two exponential expressions, we can use the power of a product rule of exponents, which breaks up the power of a product of factors into the product of the powers of the factors.

Write answers with positive exponents. 2512 a.  ​ ____ ​ 2513 Finding the Power of a Product To simplify the power of a product of two exponential expressions, we can use the power of a product rule of exponents, which breaks up the power of a product of factors into the product of the powers of the factors. 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.

_ ​ ​​ ​ · ​ ​ _ ​ ​ c. t3 · t6 · t5 y y     Using the Quotient Rule of Exponents The quotient rule of exponents allows us to simplify an expression that divides two numbers with the same base but ym different exponents. In a similar way to the product rule, we can simplify an expression such as ​ ___ yn ​, where m > n. 9 y Consider the example ​ _5 ​. Perform the division by canceling common factors. y y·y·y·y·y·y·y·y·y y9 ​ ___ ​ = ​ ___ ​ y · y · y · y · y y5 ​y​ · y​​ · y​​ · y​​ · y​​ · y · y · y · y = ​ ___ ​  y​​ · y​​ · y​​ · y​​ · y​ ​ y·y·y·y = __________ ​ ​ 1 = y 4 Notice that the exponent of the quotient is the difference between the exponents of the divisor and dividend.

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