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Exponent Laws II

Exponent Laws II. Topic 2.5. OVERVIEW. POWER OF A POWER. (3 2 ) 4. = 3 2 X 3 2 X 3 2 X 3 2. What do you do with the exponents of like bases when they are multiplied together ? (Last section). =3 2x4. ADD!!! = 3 2+2+2+2. = 3 8. =3 2x4. This answer is the same as multiplying the

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Exponent Laws II

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  1. Exponent Laws II Topic 2.5

  2. OVERVIEW

  3. POWER OF A POWER (32)4 = 32X 32X 32X 32 What do you do with the exponents of like bases when they are multiplied together? (Last section) =32x4 ADD!!! = 32+2+2+2 = 38 =32x4 This answer is the same as multiplying the exponents together.

  4. POWER OF A POWER Proper Definition (na)b = naxb for any n, a, and b in the real numbers.

  5. Why don’t we just do this? (32)4 = (9)4 = 9 x 9 x 9 x 9 = 6561 Because sometimes we could get really difficult numbers.

  6. Why don’t we just do this? Because sometimes we could get really difficult numbers. (912)4 = (282429536481)4 (282429536481)x(282429536481)x (282429536481)x(282429536481) This is way harder than just doing this: (912)4 = 912x4 = 948

  7. Exponent Law for POWER OF A POWER To find a power of a power, MULTIPLY the exponents! Write each as a power. (62)7 [(-7)3]2 -(24)5 = 62x7 = (-7)3x2 = -(24x5) = = =

  8. POWER OF A PRODUCT Simplify, then evaluate. Is there another way to figure this out? =(2x3)3 =(2x3)(2x3)(2x3) Remember, you can multiply in any order, so group the same numbers =2x2x2x3x3x3 To find a power of product, DISTRIBUTE the exponents to each base! =23 x 33 =216

  9. POWER OF A PRODUCT These two methods will give you the same answer. Method 1 Method 2 (2x3)3 (2x3)3 =23 x 33 =(6)3 =216 =216 Again the numbers can get messy on you, and when you start using variables only method 1 will work

  10. POWER OF A PRODUCT Proper Definition (m x n)a = ma x na for any m, n, and a in the real numbers.

  11. POWER OF A QUOTIENT Simplify First! To find a power of QUOTIENT, DISTRIBUTE the exponents to each base, then evaluate (if you are asked to!).

  12. POWER OF A QUOTIENT Proper Definition for any m, n, and a in the real numbers.

  13. RECAP Power of a power (43)5 = 43x5 = 415 Power of a product (3x8)4 = 34 x 84 Power of a power

  14. ASSIGNMENT PAGE 84 Page 84-85 #4ace, 5ace, 6ace, 8ace, 13, 14aceg, 16ace, 21

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