Law of exponent Teacher slide

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5 May 2015
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Law of exponent Teacher slide

• 1. Law of Exponent & Solving Exponential Function By: Ms. P Algebra II, 9th grade
• 2. Introduction to Exponent Definition: Exponent of a number says how many times to use the number in a multiplication For example in 5⁴, the 4 means that we use 5 four times. So, 5⁴ = 5 x 5 x 5 x 5 x 5 Read as “five to the power of 4” Exponents are also called Power or Indices
• 3. Intro to Exponent Cont. Exponents make mathematical writing easier when use many multiplication. So in general An tells you to multiply A by itself n times. In another word, there are n of those A An = A x A x … x A n 2 is the exponent value or index or power 8 is the base value Your turn to practice; Expand and compare the difference between these two exponential terms. a) 27 and 72 b) 35 and 53 c)43 and 34
• 4. Negative Exponent A negative exponent means it tells us to divide ONE by value of A after multiplying it n times 5-1 = 1 ÷ 5 = 0.2 8-5 = 1 ÷ ( 8 x 8 x 8 x 8 x 8 ) = 1 ÷ 32,768 = 0.0000305 Can you think of another way to solve 8-5 ? That’s right, we can rewrite the denominator in exponential form, so 8-5 = 1 / 85 = 1 / 32,768 = 0.0000305 In general : “take the reciprocal exponent” What if the Exponent is 1, or 0? A1 If the exponent is 1, then you just have the number itself (example 91 = 9) A0 If the exponent is 0, then you get 1 (example 90 = 1) Your turn; Please solve a) 4-2 b)10-3 c) (-2)-3
• 5. Law of Exponents or Rules of Exponents We can add exponents (n) if we have the same multiply two values with the same base (A). Why? Remember that 5⁴ = 5 x 5 x 5 x 5 x 5 So if we want compute 5⁴ * 53 =( 5 x 5 x 5 x 5) * (5 x 5 x 5 ) =( 5 x 5 x 5 x 5 5 x 5 x 5 ) = 57 So, 5⁴ * 53 = 5⁴+3 = 57 Video Explanation https://www.youtube.com/watch?v=VQsQj1Q_ CMQ REMEMBER!
• 6. 8-5 Please pair with a classmate next to you to complete this graphic organizer of law of exponents. Please raise your hand if you have any questions Paired Activity- Law of Exponents
• 7. Solving Exponential Equation As you complete solve these equations, please answer the following questions; 1) Identify the base and the power 2) Please simplify and solve, if possible. 3) What law of exponent did you use? Please state the reason if a problem cannot be solved Work must be shown. i) (x½)6 ii)(2½)4 * (2¼)8 iii) (3½)6 * (4½)8 iiv)(2¼)16 * (4½)8 (3)2 * 42
• 8. Rewrite exponential expression Think of how you may solve for this problem; Solve 5x = 53 , Find x That’s right! Both have the same base of “5” thus the only way the two expression can be equal to each other for their power or exponent to be the same, Therefore, x = 3 What if the bases are not the same? Can we still solve the equation? Think of this problem 5x=253 We know the bases are not the same, but can we rewrite 25 to have a base of 5? 25 can be written as 52 Therefore, we can rewrite the equation so they have a common base as 5x=253 5x=(52)3 5x=56 Simplify x = 6 Solve for x
• 9. Rewrite exponential expression Cont. Now examine this problem. What if the exponent is negative? And the base is a fraction? (1/2)x = 4 , solve for x (1/2)x = 2 -1x quotient law of exponent 4 = 22 rewrite 4 to have a common base of 2 2-1x =22 substituting to original equation 2-x = 22 Simplify -x = 2 Solve for x Therefore, x = -2
• 10. Solving Exponential Expression Please write down the reason for each step to solve the exponential equations; (As I just did in the previous example) 1) 9x=81 2) (1/4)x = 32 3) 4 2x+1 = 65 4) (1/9)x – 3 = 24
• 11. Next Lesson: Tomorrow we will go over 1) Standard form of Exponential function 2) Graphing of exponential function

Notes de l'éditeur

1. 42x+1−1=65−142x+1=64