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Laws of Indices

Laws of Indices. The Algebra Recap Lesson Made by Yue Jun (2011) Courtesy to various sources. What are indices?. The indice of a number says how many times to use the number in a multiplication. Also known as powers or exponents (must know all the three different terms)

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Laws of Indices

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  1. Laws of Indices The Algebra Recap Lesson Made by Yue Jun (2011) Courtesy to various sources

  2. What are indices? The indice of a number says how many times to use the number in a multiplication. Also known as powers or exponents (must know all the three different terms) Example:82 = 8 x 8 = 64 Read as “8 to the power of 2” or simply “8 squared”

  3. Practice Question Simplify: a x a x a x a x a x a x a Answer: a7

  4. Law 1 x1 = x What is 6 to the power of 1? Answer: 61 = 6

  5. Law 2 x0 = 1 What is 4 to the power of 0? Answer: 40 = 1

  6. Law 3 x-1 = 1/x What is 3 to the power of -1? Answer: 3-1 = 1/3

  7. Law 4 x-n = 1/xn What is 4 to the power of -2? Answer: 4-2 = 4/22 = 4/4 = 1

  8. Finding the Identity What is y3y2? Answer: y3y2 = (y x y x y)(y x y) = y5 Find the relationship between the powers of the question and answer. Answer: 3 + 2 = 5

  9. Law 5 xmxn = xm+n What is 3 to the power of 72 multiplied by 3 to the power of 41? Leave your answer in indices form. Answer: 372341 = 372+41 = 3113

  10. Finding the Identity What is y5/y2? Answer: y5/y2 = (y x y x y x y x y)/(y x y) = y3 Find the relationship between the powers of the question and answer. Answer: 5 - 2 = 3

  11. Law 6 xm/xn = xm-n What is 2 to the power of 81 multiplied by 2 to the power of 24? Leave your answer in indices form. Answer: 281224 = 281-24 = 257

  12. Finding the Identity What is (y3)2? Answer: (y3)2 = (y x y x y)(y x y x y) = y6 Find the relationship between the powers of the question and answer. Answer: 3 x 2 = 6

  13. Law 7 (xm)n = xmn What is (2 to the power of 4) to the power of 3? Answer: (24)3 = 2(4)(3) = 212

  14. Finding the Identity What is 2232? Answer: 2232 = 4 x 9 = 36 = 62 Find the relationship between the bases of the question and answer. Answer: 2 x 3 = 6

  15. Law 8 xmym = (xy)m What is 2 to the power of 54 multiplied by 4 to the power of 54? Leave in indices form. Answer: 254454 = (2x4)54 = 854

  16. Finding the Identity What is 42/22? Answer: 42/22 = 16/4 = 4 = 22 Find the relationship between the bases of the question and answer. Answer: 4 / 2 = 2

  17. Law 9 xm/ym = (x/y)m What is 6 to the power of 67 multiplied by 2 to the power of 67? Leave in indices form. Answer: 667/267 = (6/2)67 = 367

  18. Nine Laws of Indices x1 = x x0= 1 x-1 = 1/x x-n= 1/xn xmxn = xm+n xm/xn = xm-n (xm)n = xmn xmym = (xy)m xm/ym = (x/y)m

  19. Additional Reading http://www.mathsisfun.com/algebra/exponent-laws.html

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