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Lesson Menu. Main Idea and New Vocabulary Example 1: Write Expressions Using Powers Example 2: Write Expressions Using Powers Example 3: Write Expressions Using Powers Example 4: Write Expressions Using Powers Example 5: Write Expressions Using Powers Example 6: Evaluate Powers

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  1. Lesson Menu Main Idea and New Vocabulary Example 1: Write Expressions Using Powers Example 2: Write Expressions Using Powers Example 3: Write Expressions Using Powers Example 4: Write Expressions Using Powers Example 5: Write Expressions Using Powers Example 6: Evaluate Powers Example 7: Evaluate Powers Example 8: Real-World Example Key Concept: Order of Operations Example 9: Evaluate Algebraic Expressions Example 10: Evaluate Algebraic Expressions

  2. Use powers and exponents to write large and small numbers. • power • base • exponent Main Idea/Vocabulary

  3. Write Expressions Using Powers Write 7 • 7 • 7 • 7 using exponents. The base 7 is a factor 4 times. So, the exponent is 4. 7 • 7 • 7 • 7 = 74 Answer: 74 Example 1

  4. Write 11 • 11 • 11 • 11 •11 •11 using exponents. A. 6 • 11 B. 611 C. 116 D. 117 Example 1 CYP

  5. Write Expressions Using Powers Write (–9)(–9)(–9) using exponents. The base –9 is a factor 3 times. So, the exponent is 3. (–9)( –9)(–9)= (–9)3 Answer: (–9)3 Example 2

  6. Write (–4)(–4)(–4)(–4)(–4) using exponents. A. (–4)4 B. (–4)5 C. (–4)(5) D. 5–4 Example 2 CYP

  7. Write Expressions Using Powers Write a• a • a • a • a using exponents. The base a is a factor 5 times. So, the exponent is 5. a • a • a • a • a = a5 Answer: a5 Example 3

  8. Write y • y • y • y • y • y • y using exponents. A.y7 B.y6 C. 7y D. 7y Example 3 CYP

  9. Write Expressions Using Powers Write 4 • 4 • 6 • 6 • 6 • 6 • 6 using exponents. 4 • 4 • 6 • 6 • 6 • 6 • 6 = (4 • 4) • (6 • 6 • 6 • 6 • 6)Associative Property = 42 • 65Definition of exponents Answer: 42 • 65 Example 4

  10. Write (–2) • (–2) • (–2) • 7 • 7 using exponents. A. (–2) • 7 B. (–2)3• 73 C. (–2)3• 72 D. (–2)(3) • 72 Example 4 CYP

  11. Write Expressions Using Powers Write x• y • x • y • x •x using exponents. x • y • x • y • x • x = x • x • x • x • y • yCommutative Property = (x • x • x • x)•(y • y) Associative Property = x4 • y2Definition of exponents Answer: x4 • y2 Example 5

  12. Write j • j • k • k • j using exponents. A.j•k B. 3j• 2k C.j3•k2 D.j2•k3 Example 5 CYP

  13. Evaluate Powers Evaluate (–5)2. (–5)2 = (–5) • (–5) Write the power as a product. = 25 Multiply. Answer: 25 Example 6

  14. Evaluate (–4)5. A.–1,024 B.–20 C.625 D.1,024 Example 6 CYP

  15. Evaluate . Write the power as a product. Multiply. Answer: Evaluate Powers Example 7

  16. Evaluate . A. B. C. D. Example 7 CYP

  17. RACQUETBALLA racquetball court has an area of 2 • 42• 52square feet. What is the area of the racquetball court? 2 • 42 • 52 = 2 • 4 • 4 • 5 • 5 Write the power as a product. = 2 • (4 • 4) • (5 • 5) Associative Property = 2 • 16 • 25 or 800 Multiply. Answer: The racquetball court has an area of about 800 square feet. Example 8

  18. GARDENSA community vegetable garden has an area of 3 • 43• 62 square feet. What is the area of the garden? A.72 square feet B.1,152 square feet C.1,296 square feet D.6,912 square feet Example 8 CYP

  19. Key Concept 9

  20. Evaluate Algebraic Expressions Evaluate x3 + y5 if x = 4 and y = 2. x3 + y5 = 43 + 25Replace x with 3 and y with 2. = (4 • 4 • 4) + (2 • 2 • 2 • 2 • 2) Write the powers as products. = 64 + 32 or 96 Add. Answer: 96 Example 9

  21. Evaluate a4 – b2 if a = 3 and b = 5. A.76 B.56 C.4 D.2 Example 9 CYP

  22. Evaluate Algebraic Expressions Evaluate (x + y)2 if x = 4 and y = 2. (x + y)2 = (4 + 2)2Replace x with 4 and y with 2. = 62 Perform operations in the parentheses first. = 6 • 6 or 36 Write the powers as products. Then simplify. Answer: 36 Example 10

  23. Evaluate (r + s)4 if r = –3 and s = 7. A.64 B.81 C.256 D.10,000 Example 10 CYP

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