Negative exponents – moving the exponential factor to the denominator creates a positive exponent ! Rule #2: Dividing Powers with the Same Base. When dividing powers with the same base you SUBTRACT the exponents. Vocabulary: Monomial A number, a variable, or a product of a number and one or more variables Examples: 34xy, 7a2b Power 5 2 Exponent Base Rules of Exponents: Product of Powers: m x na m n Properties of Exponents Packet Warm ups… Write each expression using an exponent. xxm mn n Example 3: (x2y3)4 = x2 4 y3 4 = x8y12 Example 4: (2x3yz2)3 = 23 x3 3 y3 z2 3 = 8x9y3z6 Quotient Rule: When dividing monomials that have the same base, subtract the exponents. You will probably not cover all the rules on the first day. Practice is provided on the notes 4. B. C. 2. 6−2 4. −7 Now that we know negative exponents mean reciprocal, we can perform operations with negative exponents just like we did with positive exponents. Simplify means to combine like terms using the laws of exponents. This packet provides practice in exponents and roots as they appear on high school equivalency exams. 222 2. xxxx 3. QUOTIENT RULE: To divide when two bases are the same, write the base and SUBTRACT the exponents. This topic is introduced with an exploration of multiplication, factors, multiples, prime numbers and composite numbers, which then leads into prime factorization and representation of repeated multiplication through exponents. When multiplying powers with the same base you ADD the exponents. 2−3 3. DIVISION PROPERTIES QUOTIENT OF POWERS This property is used when dividing two … Power Rule: When raising monomials to powers, multiply the exponents. Bright Looking at powers of 10, Let’s now state the rule: 1. −6 2. The Exponent Rules. Examples: A. … m mn n x x x Example 5: 3 3 ( 2) 5 2 x xx x Example 6: 6 6 2 4 2 5 55 5 EXPONENT RULES & PRACTICE 1. Example: a5 a3 = a5 – 3 = a2. (This is two half sheets on one page) 5. You just cannot leave negative powers in the final answer. Your answer should contain only positive exponents. For example: x² × x³, 2³ × 2⁵, (-3)² × (-3)⁴ In multiplication of exponents if the bases are same then we need to add the exponents. The laws of exponents are explained here along with their examples. Examples: A. Example: a3 x a2 = a3 + 2 = a5. or "! The resources in this packet have been compiled from the Regional Professional Development Program and Mr. Also, you may work with negative powers as you are simplifying within the problem. A Practice worksheet which covers Rule #1 and #2 only. MULTIPLICATION PROPERTIES SUMMARY PRODUCT OF POWERS POWER TO A POWER POWER OF PRODUCT ADD THE EXPONENTS MULTIPLY THE EXPONENTS DISTRIBUTE THE EXPONENT ZERO AND NEGATIVE EXPONENTS ANYTHING TO THE ZERO POWER IS 1. To 1. 33x x x y y y y Write each expression without using an exponent. Rule #1: Multiplying Powers with the Same Base. 1. A homework assignment which covers Rule #1 and #2 only. 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