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Working with Powers

Learn how to simplify expressions with integer exponents, apply exponent rules, and perform operations with exponents. Understand the concept of repeated multiplication and use exponential notation. Explore combining and dividing exponents. Master the distributive rule for exponents.

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Working with Powers

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  1. Working with Powers • Integer Exponents • Exponent Rules • Order of Operations

  2. Examples • 2 × 2 = • 2 × 2 × 2 = • 2 × 2 × 2 × 2 = • How can we write these in shorter notation?

  3. 3 × 3 × 3 × 3 × 3 = Examples • Multiplication is a shortcut for repeated addition. • Exponents are a shortcut for repeated multiplication. 3 + 3 + 3 + 3 + 3 = 5 × 3

  4. Write these numbers using exponential notation: • 10,000 = 10? • 27 = 3? • 32 = 2?

  5. Computer Memory A byte is capable of storing one letter of the alphabet. For example, the word “math” requires four bytes to store in a computer. Bytes of computer memory are often manufactured in amounts equal to powers of 2.

  6. For Example 1 kilobyte (1K) = 210 = 1 megabyte (1 MB) = 220 =

  7. Integer Exponents • Base 4 • Exponent 3 • 43 is called a power • 43 = 4 x 4 x 4 • = 64

  8. You try these . . . • 72 • 54 • 210

  9. Operations with Exponents • Multiply (x3)∙(x4) = (x ∙ x ∙ x) ∙ (x ∙ x ∙ x ∙ x) = (x ∙ x ∙ x ∙ x ∙ x ∙ x ∙ x) = x7 A5∙ A4 = • Divide:

  10. Exponent Rules #1 n times

  11. Zero as an exponent • 40 • 90 • 170

  12. Exponent Rules #2

  13. a0 = 1 • M0 • (pq)0 • (2x2y)0

  14. 3-1 7-1 5-2 2-4 (1/2) -1 (3/4) -2 Negative Exponents

  15. Exponent Rules #3

  16. M-2 • x-5 • (1/y)-3

  17. Combining Exponents aman=?

  18. Exponent Rules #4

  19. y-2y7 m6m-6 2z-3z5w-6w-2 • x5x4 • b3b-6 • (2x3)(4x-2)

  20. Combining Exponents am/an=?

  21. Exponent Rules #5

  22. Combining Exponents (am)n=?

  23. Exponent Rules #6

  24. (w4)5 • (p-3)4 • (5x4)-2 • (-3y-7)3

  25. Combining Exponents

  26. Exponent Rules #7 (distributive rule for exponents)

  27. Exponent Rules • 1. • 2. • 3.

  28. 4. 5. 6. 7. Exponent Rules

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