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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Section 1.3 Integer Exponents

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Objectives Bases and Positive Exponents Zero and Negative Exponents Product, Quotient, and Power Rules Order of Operations Scientific Notation

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Bases and Positive Exponents The expression 8 2 is an exponential expression with base 8 and exponent 2. Exponent Base

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Using the given base, write each number as an exponential expression. a. 100,000 (base 10)b. 128 (base 2) Solution a. 100,000 b. 128

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Let a and b be nonzero real numbers and m and n be positive integers. Then INTEGER EXPONENTS

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Simplify each expression. a.b.c.d. Solution a. b. c. d.

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. For any number a and integers m and n, THE PRODUCT RULE

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Multiply and simplify. Use positive exponents. a. b. c. d. Solution a. b. c. d.

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. For any nonzero number a and integers m and n, THE QUOTIENT RULE

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Simplify each expression. Use positive exponents. a. b. c. d. Solution a. b. c. d.

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. For any real number a and integers m and n, RAISING POWERS TO POWERS

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Simplify each expression. Use positive exponents. a.b. c.d.

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. For any real numbers a and b and integer n, RAISING PRODUCTS TO POWERS

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Simplify each expression. Use positive exponents. a.b. c.d.

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. For nonzero numbers a and b and any integer n, RAISING QUOTIENTS TO POWERS

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Simplify each expression. Use positive exponents. a.b. c.d.

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Using the following order of operations, first perform all calculations within parentheses and absolute values, or above and below the fraction bar. Then use the same order of operations to perform the remaining calculations. 1. Evaluate all exponential expressions. Do any negations after evaluating exponents. 2. Do all multiplication and division from left to right. 3. Do all addition and subtraction from left to right. ORDER OF OPERATIONS

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Evaluate each expression. a. b.

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. A real number a is in scientific notation when a is written as b 10 n, where 1 |b| < 10 and n is an integer. SCIENTIFIC NOTATION

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1. Move the decimal point in a number a until it represents a number b such that 1 b < Count the number of decimal places that the decimal point was moved. Let this positive integer be n. (If the decimal point is not moved, then a = a 10 0.) 3. If the decimal point was moved to the left, then a = b 10 n. If the decimal point was moved to the right, then a = b 10 -n. WRITING A POSITIVE NUMBER IN SCIENTIFIC NOTATION

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Important Powers of 10 Number Value ThousandthHundredthTenthThousandMillionBillionTrillion

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Write each number in scientific notation. a. 475,000b Solution a. 475,000b. Move the decimal point 5 places to the left. Move the decimal point 6 places to the right.

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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Write each number in standard form. a.b. Solution Move the decimal point 6 places to the right since the exponent is positive. Move the decimal point 3 places to the left since the exponent is negative.

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