Rule #1: Multiplying Powers with the Same Base. Examples: A. Examples: A. … 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. A homework assignment which covers Rule #1 and #2 only. EXPONENT RULES & PRACTICE 1. DIVISION PROPERTIES QUOTIENT OF POWERS This property is used when dividing two … Also, you may work with negative powers as you are simplifying within the problem. A Practice worksheet which covers Rule #1 and #2 only. The resources in this packet have been compiled from the Regional Professional Development Program and Mr. Rules of Exponents N.RN.1 I CAN… rewrite expressions involving rational exponents using the properties of exponents. Properties of Exponents Date_____ Period____ Simplify. QUOTIENT RULE: To divide when two bases are the same, write the base and SUBTRACT the exponents. Your answer should contain only positive exponents. Example: a3 x a2 = a3 + 2 = a5. 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 dividing powers with the same base you SUBTRACT the exponents. This packet provides practice in exponents and roots as they appear on high school equivalency exams. 3 4 5. xy53 6. 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 B. C. 2. Simplify means to combine like terms using the laws of exponents. 33x x x y y y y Write each expression without using an exponent. Power Rule: When raising monomials to powers, multiply the 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. 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. 75ab You have seen that exponential expressions are useful when writing very small or very large numbers. PRODUCT RULE: To multiply when two bases are the same, write the base and ADD the exponents. 222 2. xxxx 3. (expand the expression, do not simplify) 4. Properties of Exponents Packet Warm ups… Write each expression using an exponent. Example: a5 a3 = a5 – 3 = a2. 1. 2−3 3. To Bright Looking at powers of 10, Let’s now state the rule: 1. −6 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. (This is two half sheets on one page) 5. 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