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Power of Multiplication and Division: Simplifying Expressions

Learn to simplify expressions involving powers by multiplying and dividing monomials. Understand properties. Practice examples. Find common bases, add exponents, and simplify real number expressions.

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Power of Multiplication and Division: Simplifying Expressions

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  1. Lesson Menu Main Idea and New Vocabulary Key Concept: Product of Powers Example 1: Multiply Powers Example 2: Multiply Powers Example 3: Multiply Powers Key Concept: Quotient of Powers Example 4: Divide Powers Example 5: Divide Powers Example 6: Real-World Example Example 7: Simplify Expressions

  2. Simplify real number expressions by multiplying and dividing monomials. • monomial Main Idea/Vocabulary

  3. Key Concept

  4. Multiply Powers Simplify 76 • 7. Express using exponents. 76 • 7 = 76 • 717 = 71 = 76 + 1 The common base is 7. = 77 Add the exponents. Example 1

  5. Multiply Powers Check76 · 7 = (7 · 7 · 7  7 · 7 · 7) · 7 = 7 · 7 · 7  7 · 7 · 7 · 7 = 77 Answer: 77 Example 1

  6. Simplify 8• 85. Express using exponents. A. 84 B. 85 C. 86 D. 88 Example 1 CYP

  7. Multiply Powers Simplify r4•r6. Express using exponents. r4 • r6 = r4 + 6The common base is r. = r10 Add the exponents. Answer: r10 Example 2

  8. Simplify t9 • t2. Express using exponents. A.t4.5 B.t7 C.t11 D.t18 Example 2 CYP

  9. Multiply Powers Simplify –7x2 • 11x4. Express using exponents. –7x2 • 11x4 = (–7 • 11)(x2 • x4)Commutative and Associative Properties = (–77)(x2 + 4)The common base is x. = –77x6Add the exponents. Answer: –77x6 Example 3

  10. Simplify 4n6(–2n5). Express using exponents. A. –8n30 B. –8n11 C. 8n30 D. 8n Example 3 CYP

  11. Key Concept 4

  12. Simplify . Express using exponents. Divide Powers = 612 – 2The common base is 6. = 610 Simply. Answer: 610 Example 4

  13. Simplify . Express using exponents. A. 82 B. 85 C. 815 D. 8–5 Example 4 CYP

  14. Simplify . Express using exponents. Divide Powers = a14 – 8The common base is a. = a6 Simply. Answer: a6 Example 5

  15. Simplify . Express using exponents. A.h4 B.h14 C.h15 D.h20 Example 5 CYP

  16. MEASUREMENTOne centimeter is equal to 10 millimeters, and one kilometer is equal to 106millimeters. How many centimeters are in one kilometer? 10 = 101 = 106 – 1 or 105Quotient of Powers Answer: There are 105 centimeters in one kilometer. Example 6

  17. MEASUREMENTOne metric ton is equal to 106 grams and one hectogram is equal to 102 grams. How many times greater is a metric ton than a hectogram? A.103times greater B.104times greater C.108times greater D.1012times greater Example 6 CYP

  18. Simplify Simplify Expressions Group by common base. = 21 • 52• 91 Subtract the exponents. = 2• 25• 9 52 = 25 = 450 Simplify. Answer: 450 Example 7

  19. Simplify . Express using exponents. A.144 B.1,152 C.1,536 D.9,116 Example 7 CYP

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