Law of exponent Lecture Slide
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Transcript of Law of exponent Lecture Slide
![Page 1: Law of exponent Lecture Slide](https://reader035.fdocuments.in/reader035/viewer/2022062221/55d18cc1bb61eb7f6f8b4820/html5/thumbnails/1.jpg)
Law of Exponent &Solving Exponential
FunctionBy: Ms. P
Algebra II, 9th grade
![Page 2: Law of exponent Lecture Slide](https://reader035.fdocuments.in/reader035/viewer/2022062221/55d18cc1bb61eb7f6f8b4820/html5/thumbnails/2.jpg)
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
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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
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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 = 0.28-5 = 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 solvea) 4-2 b)10-3 c) (-2)-3
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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 5So 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 Explanationhttps://www.youtube.com/watch?v=VQsQj1Q_CMQ
REMEMBER!
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Law of Exponents or Rules of Exponents Cont.
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 5So 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 Explanationhttps://www.youtube.com/watch?v=VQsQj1Q_CMQ
![Page 7: Law of exponent Lecture Slide](https://reader035.fdocuments.in/reader035/viewer/2022062221/55d18cc1bb61eb7f6f8b4820/html5/thumbnails/7.jpg)
Solving Exponential Equation
As you complete solve these equations, please answer the following questions;1)Identify the base and the power2)Please simplify and solve, if possible. 3)What law of exponent did you use? Please state the reason if a
problem cannot be solvedWork must be shown.
i) (x½)6 ii)(2½)4 * (2¼)8
iii) (3½)6 * (4½)8 iiv)(2¼)16 * (4½)8
(3)2 * 42
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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 as5x=253 5x=(52)3
5x=56 Simplifyx = 6 Solve for x
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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 exponent4 = 22 rewrite 4 to have a common base of 22-1x =22 substituting to original equation2-x = 22 Simplify-x = 2 Solve for x
Therefore, x = -2
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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
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Next Lesson:
Tomorrow we will go over 1) Standard form of Exponential function 2) Graphing of exponential
function