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Multiplication Rules for Exponents

Multiplication Rules for Exponents. How do I multiply powers with the same base? How do I simplify a power to a power?. Multiplication Rules for Exponents Essential Questions. Multiplication of Exponents. Copy the text below in to your books and then answer the questions. 2 5 x 2 2 =

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Multiplication Rules for Exponents

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  1. Multiplication Rules for Exponents

  2. How do I multiply powers with the same base? How do I simplify a power to a power? Multiplication Rules for Exponents Essential Questions

  3. Multiplication of Exponents Copy the text below in to your books and then answer the questions • 25 x 22 = • 43 x 46 = • 62 x 6= • 84 x 83 = • 92 x 9-2 = • 2-3 x 2 = • 55 x 5–7 = • 3-2 x 3= • 8-2 x 8-3 = When multiplying: Powers of the same base (number) are added. In general: am x an = am+n When multiplying: Powers of the same base (number) are added. In general: am x an = am+n Base number Power Give your answer in power form Example: 55 x 56= 511

  4. Multiplying powers of the same number Answers 27 49 63 87 90 = 2-2 = 5-2 = 3-1 = 81= • 25 x 22 = • 43 x 46 = • 62 x 6= • 84 x 83 = • 92 x 9–2 = • 2-3 x 2= • 55 x 5–7 = • 3 -2 x 3= • 8-2 x 8-3 = When multiplying: Powers of the same base (number) are added. In general: am x an = am+n Base number Power

  5. Power-of-a-Power Property For all nonzero real numbers x and all integers m and n, (xm)n = xmn. Rules and Properties (x2)4 = x8 Example: 1. (x3)x = x3x 2. (xy4)3 = x3y12 3.

  6. Rules and Properties Power-of-a-Product Property For all nonzero real numbers x and y and all integers n, (xy)n = xnyn. (xy4)3 = x3y12

  7. Do These Together Simplify 4. (y3)5 = y15 m3x 5. (m3)x = 6. (x4)2 = x8 x6y3x 7. (x2yx)3 = 8. (x3y2)4 = x12y8

  8. TRY THESE Simplify 9. (y4)4 = y16 mxy 10. (my)x = 11. (x3)7 = x21 x5xy3x 12. (x5y3)x = 13. (x2y5)7 = x14y35

  9. Powers of –1 Even powers of –1 are equal to 1. Odd powers of –1 are equal to –1. Rules and Properties Examples: (-2)2 = 4 -22 = -4 14. 15. (-2)3 = -8 -23 = -8 17. 16. -27x12y6 (-3x4y2)3= 19. 4x4y6 18. (-2x2y3)2=

  10. Do These Together Simplify 20. (2y2)3 = 8y6 21. (-2m4)4 = 16m16 22. (-x2)5 = -x10 -x12y18 23. (-x4y6)3 = 9x6y4 24. (-3x3y2)2 =

  11. TRY THESE Simplify 25. (3y4)2 = 9y8 26. (-3m2)3 = -27m6 27. (-x3)4 = x12 -x6y12 28. (-x2y4)3 = 16x4y6 29. (-4x2y3)2 =

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