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Laws of Exponents: Powers and Products Multiplication Rules for Exponents Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Laws of Exponents: Powers and Products Multiplication Rules for Exponents Essential Questions • How do I multiply powers with the same base? • How do I simplify a power to a power? Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Laws of Exponents: Powers and Products Multiplication of Exponents Copy the text below in to your books and then answer the questions a) 25 x 22 = When multiplying: Powers of the same base (number) are added. m x an n = am+n In general: am am+n Base number Power b) c) d) e) f) g) h) i) 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 = Give your answer in power form Example: 55 x 56= 511 Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Laws of Exponents: Powers and Products Multiplying powers of the same number Answers When multiplying: Powers of the same base (number) are added. In general: am x an = am+n Base number Power a) b) c) d) e) f) g) h) i) 7 2 2 x2 = 9 4 3 6 4 x4 = 3 62 x 6 = 6 7 84 x 83 = 8 0 92 x 9 –2 = 9 = -2 = 2 -3 2 x2 = -2 = 5 5 –7 5 x5 = -1 3 -2 x 3 = 3 = 1 8 -2 x 8 -3 = 8 = 5 2 Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Laws of Exponents: Powers and Products Rules and Properties Power-of-a-Power Property For all nonzero real numbers x and all integers m and n, (xm)n = xmn. Example: 1. (x2)4 = x8 2. (x3)x = x3x 4 3 3 12 3. (xy ) = x y Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Laws of Exponents: Powers and Products 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 Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Laws of Exponents: Powers and Products Do These Together Simplify 4. (y3)5 = y15 5. (m3)x = m3x 6. (x4)2 = x8 7. (x2yx)3 = x6y3x 8. (x3y2)4 = x12y8 Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Laws of Exponents: Powers and Products TRY THESE Simplify 9. (y4)4 = y16 10. (my)x = mxy 11. (x3)7 = x21 12. (x5y3)x = x5xy3x 13. (x2y5)7 = x14y35 Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Laws of Exponents: Powers and Products Rules and Properties Powers of –1 Even powers of –1 are equal to 1. Odd powers of –1 are equal to –1. Examples: 14. (-2)2 = 4 16. (-2)3 = -8 18. (-2x2y3)2= 4x4y6 15. -22 = -4 17. -23 = -8 19. (-3x4y2)3= -27x12y6 Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Laws of Exponents: Powers and Products Do These Together Simplify 20. (2y2)3 = 8y6 21. (-2m4)4 = 16m16 22. (-x2)5 = -x10 23. (-x4y6)3 = -x12y18 24. (-3x3y2)2 = 9x6y4 Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Laws of Exponents: Powers and Products TRY THESE Simplify 25. (3y4)2 = 9y8 26. (-3m2)3 = -27m6 27. (-x3)4 = x12 28. (-x2y4)3 = -x6y12 29. (-4x2y3)2 = 16x4y6 Copyright © by Holt, Rinehart and Winston. All Rights Reserved.