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Welcome to your personal lesson about the laws of exponents. I hope you enjoy your experience! Here are some things you need to know: 1. You will need a high speed internet connection to take advantage of the whole lesson. 2. When you see this button, it will take you to the base camp (which you will see on the next page). 3. When you see this button, it will take you to the next slide. 4. When you see this button, it will take you back to the slide you just viewed. Lets get started!

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Exponents in Action (Video) To the Laws! Quiz Me! Id rather read about it Short and sweet- Summary of rules Sing me the rules Base Camp Lets Play! Back to Introduction Listen and see! Practice makes perfect!

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Video Introducing Exponents 1.Click on the link above. You will be taken to a blog about introducing exponents. 2.In the first paragraph, there is a link to an algebra lesson by NROC Algebra 1An Open course, Unit 7, Lesson 1, Topic 1: Rules of Exponents. Click on the link. 3.Click on LOG IN AS GUEST. 4.On the new webpage, click on the PRESENTATION link.

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Practice makes perfect! Introducing Exponents 1.Click on the link above. You will be taken to a blog about introducing exponents. 2.In the first paragraph, there is a link to an algebra lesson by NROC Algebra 1An Open course, Unit 7, Lesson 1, Topic 1: Rules of Exponents. Click on the link. 3.Click on LOG IN AS GUEST. 4.On the new webpage, click on the WORKED EXAMPLES link. 5.After viewing the examples, click on the PRACTICE link.

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Listen and See Exponent Tutorials Click on the above link to visit a webpage with various tutorials about the different laws of exponents. Explore any or all of them for better understanding!

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Exponent Game Exponent Battleship

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Exponent Song Sing me the Rules!

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Reading Let's Learn the Exponential Laws

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Quiz Me! Quiz #1 Quiz #2 Quiz #3 1.For QUIZ #3, click on the link above. You will be taken to a blog about introducing exponents. 2.In the first paragraph, there is a link to an algebra lesson by NROC Algebra 1An Open course, Unit 7, Lesson 1, Topic 1: Rules of Exponents. Click on the link. 3.Click on LOG IN AS GUEST. 4.On the new webpage, click on the REVIEW link.

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Laws of Exponents Law 1 Law 2 Law 3Law 6 Law 5 Law 4Law 7 Law 8 Law 9

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Law 1 x 1 = x Any number raised to the power of 1 equals itself. Show me more! Back to the laws!

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Law 1 - examples x 1 = x Back to the laws! 10 1 = 10 6 1 = 6 129 1 = 129 3 1 = 3 z 1 = z b 1 = b y 1 = y t 1 = t

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My turn to practice. Law: x 1 = x Back to the laws! Q1:8 1 = ? 1 87 9

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Great job! You did it! On to the next problem! Back to the laws! Thats right! Any number raised to the power of one is itself, so 8 1 = 8.

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My turn to practice. Law: x 1 = x Back to the laws! Q2:r 1 = ? s 1t r

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Super! Back to the laws! Thats right! Any number raised to the power of one is itself, so r 1 = r. On to the next law!

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Oops! Try again! Back to the problem! Remember, any number raised to the power of one is itself!

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Law 2 Any number (except 0) raised to the power of 0 equals 1. x 0 = 1 Show me more! Back to the laws!

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Law 2 - examples x 0 = 1 Back to the laws! 10 0 = 1 6 0 = 1 129 0 = 1 3 0 = 1 z 0 = 1 b 0 = 1 y 0 = 1 t 0 = 1

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My turn to practice. Law: x 0 = 1 Back to the laws! Q1:8 0 = ? 1 880 0

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Yay! Back to the laws! Thats right! Any number raised to the power of zero is 1, so 8 0 = 1. On to the next problem!

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My turn to practice. Law: x 0 = 1 Back to the laws! Q2:t 0 = ? s t1 10

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Good job! Back to the laws! Thats right! Any number raised to the power of zero is 1, so t 0 = 1. On to the next law!

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Not yet! Try again! Back to the problem! Remember, any number raised to the power of zero is 1.

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Law 3 Any number raised to the power of -1 equals its reciprocal (multiplicative inverse). x -1 = 1/x where x 0 Show me more! Back to the laws!

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Law 3 - examples x -1 = 1/x where x 0 Back to the laws! 10 -1 = 1/10 6 -1 = 1/6 129 -1 = 1/129 3 -1 = 1/3 z -1 = 1/z b -1 = 1/b y -1 = 1/y t -1 = 1/t

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My turn to practice. Law: x -1 = 1/x Back to the laws! Q1:4 -1 = ? 41 14-4 1/4

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You did it! Back to the laws! Thats right! Any number raised to the power of -1 is 1 over itself (its reciprocal), so 4 -1 = 1/4. On to the next problem!

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My turn to practice. Law: x -1 = 1/x Back to the laws! Q2:z -1 = ? z -z1/z z/z

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Looking good! Back to the laws! Thats right! Any number raised to the power of -1 is one over itself (its reciprocal), so z -1 = 1/z. On to the next law!

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Think again! Back to the problem! Remember, any number raised to the power of -1 is 1 over itself (its reciprocal).

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Law 4 Any number raised to a power multiplied by that same number raised to another power equals the same number raised to the sum of the powers. x m x n = x m+n Show me more! Back to the laws!

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Law 4 - examples x m x n = x m+n Back to the laws! 10 4 10 5 = 10 9 6 3 6 7 = 6 10 129 2 129 5 = 129 7 3 6 3 8 = 3 14 x 5 x 8 = x 13 b 2 b 4 = b 6 y 1 y 4 = y 5 t 2 t 3 = t 5

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My turn to practice. Law: x m x n = x m+n Back to the laws! Q1:5 2 5 8 = ? 5 10 10 25 10 10 28

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Yippee! Back to the laws! Thats right! Any number raised to a power multiplied by the same number raised to another power is equal to that same number raised to the sum of the powers. So, 5 2 5 8 = 5 10 On to the next problem!

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My turn to practice. Law: x m x n = x m+n Back to the laws! Q2:v 3 v 6 = ? v 18 v3v3 v 36 v9v9

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Not quite! Back to the problem! Remember, any number raised to a power multiplied by the same number raised to another power is equal to that same number raised to the sum of the powers.

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Couldnt be better! Back to the laws!On to the next law! Thats right! Any number raised to a power multiplied by the same number raised to another power is equal to that same number raised to the sum of the powers. So, v 3 v 6 = v 9

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Law 5 Any number raised to a power divided by that same number raised to another power equals the same number raised to the difference of the powers. x m /x n = x m-n Show me more! Back to the laws!

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Law 5 - examples x m /x n = x m-n Back to the laws! 10 7 /10 5 = 10 2 6 3 /6 1 = 6 2 129 4 /129 2 = 129 2 3 9 /3 5 = 3 4 x 9 /x 2 = x 7 b 6 /b 3 = b 3 y 8 /y 4 = y 4 t 9 /t 3 = t 6

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My turn to practice. Law: x m /x n = x m-n Back to the laws! Q1:5 7 /5 4 = ? 5 11 5 74 5353 10 3

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You are so right! Back to the laws! Thats right! Any number raised to a power divided by the same number raised to another power is equal to that same number raised to the difference of the powers. So, 5 7 /5 4 = 5 3 On to the next problem!

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My turn to practice. Back to the laws! Q2:v 8 /v 6 = ? v 86 v2v2 v 10 v 14 Law: x m /x n = x m-n

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Lets try that again! Back to the problem! Remember, any number raised to a power divided by the same number raised to another power is equal to that same number raised to the difference of the powers.

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Wow! Back to the laws!On to the next law! Thats right! Any number raised to a power divided by the same number raised to another power is equal to that same number raised to the difference of the powers. So, v 8 /v 6 = v 2

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Law 6 Any number raised to a power then raised to another power equals the same number raised to the product of the powers. (x m ) n = x mn Show me more! Back to the laws!

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Law 6 - examples (x m ) n = x mn Back to the laws! (10 7 ) 5 = 10 35 (6 3 ) 4 = 6 12 (129 2 ) 5 = 129 10 (3 6 ) 8 = 3 48 (x 2 ) 7 = x 14 (b 3 ) 5 = b 15 (y 7 ) 3 = y 21 (t 9 ) 1 = t 9

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My turn to practice. Law: (x m ) n = x mn Back to the laws! Q1:(5 7 ) 3 = ? 5 10 5 21 15 7 35 3

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Youve got it! Back to the laws! Thats right! Any number raised to a power then raised to another power is that same number raised to the product of the powers. So, (5 7 ) 3 = 5 21 On to the next problem!

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My turn to practice. Back to the laws! Q2:(v 4 ) 8 = ? v 48 v 12 v 32 v4v4 Law: (x m ) n = x mn

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Sorry! Back to the problem! Remember, any number raised to a power then raised to another power is equal to that same number raised to the product of the powers.

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Nice work! Back to the laws!On to the next law! Thats right! Any number raised to a power then raised to another power is that same number raised to the product of the powers. So, (v 4 ) 8 = v 32

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Law 7 Any product of two numbers raised to a power equals the first number raised to the power multiplied by the second number raised to the same power. (xy) n = x n y n Show me more! Back to the laws!

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Law 7 - examples (xy) n = x n y n Back to the laws! (103) 5 = 10 5 3 5 (62) 3 = 6 3 2 3 (127) 2 = 12 2 7 2 (45) 4 = 4 4 5 4 (xz) 4 = x 4 z 4 (bc) 3 = b 3 c 3 (rs) 7 = r 7 s 7 (tu) 6 = t 6 u 6 **These numerical expressions can be simplified to a whole number.

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My turn to practice. Law: (xy) n = x n y n Back to the laws! Q1:(53) 7 = ? 57375737 53 7 157 573573

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Thats it! Back to the laws! Thats right! Any product of two numbers raised to a power equals the first number raised to the power multiplied by the second number raised to the same power. So, (53) 7 = 5 7 3 7 On to the next problem!

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My turn to practice. Back to the laws! Q2:(vt) 8 = ? 8vt vt 8 v8tv8t v8t8v8t8 Law: (xy) n = x n y n

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Lets go back! Back to the problem! Remember, any product of two numbers raised to a power equals the first number raised to the power multiplied by the second number raised to the same power.

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Youre doing great! Back to the laws!On to the next law! Thats right! Any product of two numbers raised to a power equals the first number raised to the power multiplied by the second number raised to the same power. So, (vt) 8 = v 8 t 8

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Law 8 Any quotient raised to a power equals the first number raised to the power divided by the second number raised to the power. (x/y) n = x n /y n Where y 0 Show me more! Back to the laws!

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Law 8 - examples (x/y) n = x n /y n Where y 0 Back to the laws! (10/3) 5 = 10 5 /3 5 (6/2) 3 = 6 3 /2 3 (12/7) 2 = 12 2 /7 2 (4/5) 4 = 4 4 /5 4 (x/z) 4 = x 4 /z 4 (b/c) 3 = b 3 /c 3 (r/s) 7 = r 7 /s 7 (t/u) 6 = t 6 /u 6

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My turn to practice. Law: (x/y) n = x n /y n Back to the laws! Q1:(6/4) 3 = ? 6/4 3 6/12 6 3 /4 3 6 3 /4

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Nice work! Back to the laws! Thats right! Any quotient raised to a power equals the first number raised to the power divided by the second number raised to the power. So, (6/4) 3 = 6 3 /4 3 On to the next problem!

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My turn to practice. Back to the laws! Q2:(v/t) 7 = ? 7vtv7tv7t v7t7v7t7 Law: (x/y) n = x n /y n v 7 /t 7

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Try again! Back to the problem! Remember, any quotient raised to a power equals the first number raised to the power divided by the second number raised to the power.

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Super! Back to the laws!On to the next law! Thats right! Any quotient raised to a power equals the first number raised to the power divided by the second number raised to the power. So, (v/t) 7 = v 7 /t 7

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Law 9 Any number raised to a negative power equals one over the number raised to the power. x -n = 1/x n Show me more! Back to the laws!

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Law 9 - examples x -n = 1/x n Back to the laws! 10 -5 = 1/10 5 6 -4 = 1/6 4 12 -3 = 1/12 3 4 -7 = 1/4 7 x -8 = 1/x 8 b -5 = 1/b 5 r -2 = 1/r 2 t -7 = 1/t 7

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My turn to practice. Law: x -n = 1/x n Back to the laws! Q1:8 -3 = ? 1/8 3 1/24 1/838383

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Nice job! Back to the laws! Thats right! Any number raised to a negative power equals one over the number raised to the power. So, 8 -3 = 1/8 3 On to the next problem!

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My turn to practice. Back to the laws! Q2:t -9 = ? 9t1/t 9 1/9tt9t9 Law: x -n = 1/x n

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Not yet, try again! Back to the problem! Remember, any number raised to a negative power equals one over the number raised to the power.

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Terrific! Back to the laws! Thats right! Any number raised to a negative power equals one over the number raised to the power. So, t -9 = 1/t 9

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In summary x 1 = x x 0 = 1 x -1 = 1/x x m x n = x m+n x m /x n = x m-n (x m ) n = x mn (xy) n = x n y n (x/y) n = x n /y n x -n = 1/x n

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