or "! Bright Looking at powers of 10, Let’s now state the rule: 1. −6 2. When multiplying powers with the same base you ADD the exponents. 3 4 5. xy53 6. Simplify means to combine like terms using the laws of exponents. Example: a3 x a2 = a3 + 2 = a5. Also, you may work with negative powers as you are simplifying within the problem. Rule #1: Multiplying Powers with the Same Base. 75ab You have seen that exponential expressions are useful when writing very small or very large numbers. 3 Practice Law #3: # Problem Show Your Work Exponential Form 1 2 € 35 33 3 5-3 3 2 € 46 41 3 € 76 73 4 € 63t7 9t3 Summarize Law #3: When dividing terms with exponents, if … This packet provides practice in exponents and roots as they appear on high school equivalency exams. A homework assignment which covers Rule #1 and #2 only. Properties of Exponents Date_____ Period____ Simplify. B. C. 2. 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 (This is two half sheets on one page) 5. Properties of Exponents Packet Warm ups… Write each expression using an exponent. EXPONENT RULES & PRACTICE 1. Example: a5 a3 = a5 – 3 = a2. The resources in this packet have been compiled from the Regional Professional Development Program and Mr. (expand the expression, do not simplify) 4. The laws of exponents are explained here along with their examples. When dividing powers with the same base you SUBTRACT the exponents. You will probably not cover all the rules on the first day. 33x x x y y y y Write each expression without using an exponent. Interactive Notes: Includes a review of exponents and covers the 3 rules. 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. To Negative exponents – moving the exponential factor to the denominator creates a positive exponent ! 1. Rules of Exponents N.RN.1 I CAN… rewrite expressions involving rational exponents using the properties of exponents. 2−3 3. 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. Practice is provided on the notes 4. PRODUCT RULE: To multiply when two bases are the same, write the base and ADD the exponents. The Exponent Rules. Multiplying Powers with same Base. 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. Your answer should contain only positive exponents. 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 QUOTIENT RULE: To divide when two bases are the same, write the base and SUBTRACT the exponents. You just cannot leave negative powers in the final answer. A Practice worksheet which covers Rule #1 and #2 only. 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. Power Rule: When raising monomials to powers, multiply the exponents. 1. Rule #2: Dividing Powers with the Same Base. DIVISION PROPERTIES QUOTIENT OF POWERS This property is used when dividing two … Examples: A. … 222 2. xxxx 3. 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. Examples: A. 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