By OpenStax

Algebra and Trigonometry presents a finished and multi-layered exploration of algebraic rules. The textual content is acceptable for a regular introductory Algebra & Trigonometry direction, and was once built for use flexibly. The modular technique and the richness of content material guarantees that the ebook meets the desires of numerous courses. Algebra and Trigonometry publications and helps scholars with differing degrees of training and adventure with arithmetic. principles are awarded as sincerely as attainable, and development to extra complicated understandings with enormous reinforcement alongside the way in which. A wealth of examples - often numerous dozen according to bankruptcy - provide certain, conceptual causes, that allows you to construct in scholars a powerful, cumulative origin within the fabric ahead of asking them to use what they have realized. this can be a full-color textbook.

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**Additional info for Algebra and Trigonometry**

**Example text**

When can you add two exponents? 3. What is the purpose of scientific notation? 4. Explain what a negative exponent does. NUMERIC For the following exercises, simplify the given expression. Write answers with positive exponents. 5. 92 6. 15−2 7. 32 · 33 −2 10. (5 − 8)0 2 14. 5−2 ÷ 52 9. ( 22) 13. ( 80) 11. 113 ÷ 114 8. 44 ÷ 4 12. 65 · 6−7 For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. 10 −2 612 15. 42 · 43 ÷ 4−4 16.

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.

2. Simplify. Example 8 Rationalizing a Denominator Containing a Single Term — 2√3 in simplest form. Write ______ — 3√10 Solution — — 10 √ The radical in the denominator is √ 10 . Then simplify. 10 √ — — 2 3 10 √ √ ______ — · _____ — 3√10 √ 10 — 2√30 ______ 30 — 30 √ _____ 15 36 CHAPTER 1 Prerequisites Try It #8 — 12√3 in simplest form. Write ______ — 2 √ How To… Given an expression with a radical term and a constant in the denominator, rationalize the denominator.