By OpenStax

Algebra and Trigonometry presents a entire 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 procedure 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 coaching and event with arithmetic. principles are provided as basically as attainable, and development to extra advanced understandings with massive reinforcement alongside the best way. A wealth of examples - often a number of dozen in step with bankruptcy - provide unique, conceptual factors, to be able to construct in scholars a robust, cumulative starting place within the fabric prior to asking them to use what they have realized. this can be a full-color textbook.

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**Example text**

1. Determine the power by looking at the numerator of the exponent. 2. Determine the root by looking at the denominator of the exponent. 3. Using the base as the radicand, raise the radicand to the power and use the root as the index. Example 11 Writing Rational Exponents as Radicals 2 __ Write 343 3 as a radical. Simplify. Solution The 2 tells us the power and the 3 tells us the root. 2 _ 3 — 2 3 — = √ 3432 343 343 3 = √ 37 38 CHAPTER 1 Prerequisites 3 — We know that √ 343 = 7 because 7 3 = 343.

Therefore, the exponent of 10 is 6, and it is positive because we moved the decimal point to the left. This is what we should expect for a large number. 780418 × 106 Working with small numbers is similar. 00000000000047 m. Perform the same series of steps as above, except move the decimal point to the right. 7 Be careful not to include the leading 0 in your count. We move the decimal point 13 places to the right, so the exponent of 10 is 13. The exponent is negative because we moved the decimal point to the right.

X 2 · x 5 · x 3 = x 2 + 5 + 3 = x10 Try It #1 Write each of the following products with a single base. Do not simplify further. 2 4 2 a. _ · _ 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 .