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If necessary, be sure that each base appears only once by using bm # bn = bm + n or x4 # x3 = x4 + 3 = x7 bm = bm - n. bn 4. If necessary, rewrite exponential expressions with zero powers as 1 (b0 = 1). Furthermore, write the answer with positive exponents by using b-n = 1 bn or x5 1 = x 5 - 8 = x -3 = 3 8 x x 1 = bn. b-n The following example shows how to simplify exponential expressions. Throughout the example, assume that no variable in a denominator is equal to zero. EXAMPLE 7 Simplifying Exponential Expressions Simplify: a.

If n is negative, move the decimal point in a to the left ͉ n ͉ places. 2 Exponents and Scientific Notation EXAMPLE 8 29 Converting from Scientific to Decimal Notation Write each number in decimal notation: a. 2 * 107 b. 2 * 107 c. 019 * 10-3 d. 019 * 10-3. SOLUTION In each case, we use the exponent on the 10 to determine how far to move the decimal point and in which direction. In parts (a) and (b), the exponent is positive, so we move the decimal point to the right. In parts (c) and (d), the exponent is negative, so we move the decimal point to the left.

R, e, a, l} ʝ {l, e, a, r} 28. {w, y, z} ʝ л In Exercises 29–34, find the union of the sets. 29. {1, 2, 3, 4} ʜ {2, 4, 5} 31. {1, 3, 5, 7} ʜ {2, 4, 6, 8, 10} 33. {a, e, i, o, u} ʜ л 30. {1, 3, 7, 8} ʜ {2, 3, 8} 32. {0, 1, 3, 5} ʜ {2, 4, 6} 34. {e, m, p, t, y} ʜ л In Exercises 35–38, list all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. 35. 2, 2100 6 36. 6, 0, 249 , 250 6 37. 75, 25 , p, 264 6 38.

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