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Multiply and Divide Powers - Simplify Expressions - Math Lesson

Learn how to simplify real number expressions by multiplying and dividing monomials using the laws of exponents. Practice examples and real-world applications included.

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Multiply and Divide Powers - Simplify Expressions - Math Lesson

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  1. Lesson Menu Main Idea and New Vocabulary NGSSS 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 Five-Minute Check

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

  3. MA.8.A.6.3 Simplify real number expressions using the laws of exponents. MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems. NGSSS

  4. Key Concept

  5. 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

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

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

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

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

  10. 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

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

  12. Key Concept 4

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

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

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

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

  17. 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

  18. 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

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

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

  21. Simplify 48 • 43. Express using exponents. A. 424 B. 411 C. 45 D. 4–5 Five Minute Check 1

  22. Simplify (–3x6yz2)(–2xy3). Express using exponents. A. –6x7y4z2 B. 6x6y4z2 C. 6x6y4z D. 6x7y4z2 Five Minute Check 2

  23. Simplify . Express using exponents. A. 95 B. 9–19 C. 919 D. 984 Five Minute Check 3

  24. Simplify . Express using exponents. A.a15b30 B.a8b13 C.a2b10 D.a2b7 Five Minute Check 4

  25. The population of Bangkok was 55 in 1620. By 1990, it increased 54 times. What was Bangkok’s population in 1990? A. 1,953,125 B. 6,875 C. 555,555,555 D. 390,625 Five Minute Check 5

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