Multiplication Rules for Exponents

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

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

Multiplying powers of the same number Answers 27 49 63 87 90 = 2 -2 = 5 -2 = 3 -1 = 8 1 = 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

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 (xy4)3 = x3y12 3.

Power-of-a-Product Property 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

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

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

Even powers of –1 are equal to 1. Odd powers of –1 are equal to –1. 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 15. -22 = -4 16. (-2)3 = -8 17. -23 = -8 -27x12y6 18. (-2x2y3)2= 4x4y6 19. (-3x4y2)3=

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

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