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Mastering Monomials: Multiplication and Division Rules Explained

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This guide presents clear rules for multiplying and dividing monomials, focusing on exponent manipulation. Learn how to multiply monomials with the same base by keeping the base and adding the exponents, with examples like z⁴ ⋅ z² = z⁶. For division, keep the base and subtract the exponents, such as b¹⁰ ÷ b³ = b⁷. Includes independent practice problems for reinforcement, sample questions from the ARMT exam, and a conclusion emphasizing the importance of mastering these rules. Perfect for students needing to solidify their understanding of monomials.

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Mastering Monomials: Multiplication and Division Rules Explained

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  1. Multiplying and Dividing Monomials

  2. Rules for Multiplication • When you multiply monomials and their bases are the same, you keep the base and add the exponents. • Example: z4· z2 = z4+2 = z6 • Example: 52· 59 = 52+9 = 511

  3. Independent Practice • A. n3· n2 • B. f6· f3 • C. 8 · 85 Answers: • n5 • f9 • 86

  4. Rules for Division • When you divide monomials and their bases are the same, you keep the base and subtract the exponents. • Example: b10 ÷ b3 = b10-3 = b7 • Example: 65 ÷ 6 = 65-1 = 64

  5. Independent Practice • A. w12 ÷ w5 • B. p6 ÷ p4 • C. 97 ÷ 92 Answers: • w7 • p2 • 95

  6. Sample ARMT Questions • Simplify. • 610 ÷ (67 ÷ 62) • Following the order of operations, we would take care of the parenthesis first. Since both bases are 6, we keep the base and subtract (because we are dividing). 7-2 = 5. Then we have 610 divided by 65. We have the same base so we keep it and subtract. 10 - 5 = 5. Our answer is 65.

  7. Sample ARMT Questions Cont. • 35· 38· 32 3 · 33 Simplify the top, simplify the bottom, and then divide. Since the bases are the same throughout the whole problem, we know that the base of our answer will be 3. The top gives us 35+8+2 = 315 The bottom gives us 31+3 = 34 Last we divide. We keep the base of 3 and subtract the exponents. 15 – 4 = 11. Our answer is 311.

  8. Sample ARMT Questions Cont. • Shelly drew a square and marked the lengths of the sides using exponential notation. She then wrote the expression 45 x 45 to represent the area of the square. • What is equivalent to the area, in square units, of Shelly’s square?

  9. Sample ARMT Questions Cont. 45 45 To find the area of the square, just multiply the length times the width. 45 x 45 = 45+5 = 410

  10. Conclusion • When dealing with monomials, remember to be MADS about monomials. • When you Multiply, you Add the exponents. • When you Divide, you Subtract the exponents.

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