Supplemental Worksheet Problems To Accompany: The Algebra 2 Tutor Section 13 Fractional Exponents

Transcription

1 Section Fractional Eponents Supplemental Worksheet Problems To Accompany: The Algebra 2 Tutor Section Fractional Eponents Please watch Section of this DVD before working these problems. The DVD is located at: Sample Videos For this DVD Are Located Here: Page

2 Section Fractional Eponents ) Simplify the epression: 00 2) Simplify the epression: 8 ) Simplify the epression: 9 64 Page 2

3 Section Fractional Eponents 4) Simplify the epression: ( 5) 5) Simplify the epression: 2 6 6) Simplify the epression: 52 4 Page

4 Section Fractional Eponents 7) Simplify the epression: ) Simplify the epression: 47 7 ( )( ) 9) Simplify the epression: ( 8 ) Page 4

5 Section Fractional Eponents 0) Simplify the epression: 8 ( ) 8 ) Simplify the epression: 9/7 2/7 ) Simplify the epression: /5 8/5 Page 5

6 Section Fractional Eponents ) Simplify the epression: ( 27 2/ 5 / ) 4) Simplify the epression without using any negative eponents: 8 / 5) Simplify the epression without using any negative eponents: 6 /2 Page 6

7 Section Fractional Eponents 6) Simplify the epression without using any negative eponents: 9 ( ) / 7) Simplify the epression without using any negative eponents: ( ) /4 8) Simplify the epression without using any negative eponents: 7/6 5/6 5/6 Page 7

8 Section Fractional Eponents ) Simplify the epression: For fractional eponents, you need to remember that when you see an eponent of it is equivalent to a square root. Similarly: 4 4 And so on 0 We could write a factor tree for 00, but we know from eperience that 00 0 since 0 times 0 equals 00. Ans: 0 Page 8

9 Section Fractional Eponents 2) Simplify the epression: 8 8 For fractional eponents, you need to remember that when you see an eponent of it is equivalent to a square root. Similarly: 4 4 And so on 8 Write your factor tree to simplify the cubed root and look for triplets of numbers Since this is a cubed root, then for each triplet of numbers, we pull out one. There is nothing else left under the radical, so we have arrived at the answer: Ans: 2 Page 9

10 Section Fractional Eponents ) Simplify the epression: For fractional eponents, you need to remember that when you see an eponent of it is equivalent to a square root. Similarly: 4 4 And so on You can always write the square root of a fraction as the square root of the numerator divided by the square root of the denominator. We note in the top that 9 and in the bottom This fraction can not be simplified any further. Ans: 8 Page 0

11 Section Fractional Eponents 4) Simplify the epression: ( 5) 5 For fractional eponents, you need to remember that when you see an eponent of it is equivalent to a square root. Similarly: 4 4 And so on 5 Write your factor tree to simplify the cubed root and look for triplets of numbers. Prove to yourself that this is true: ( ) ( ) ( ) Since this is a cubed root, then for each triplet of numbers, we pull out one. There is nothing else left under the radical, so we have arrived at the answer: Ans: 5 Page

12 Section Fractional Eponents 5) Simplify the epression: 2 6 ( 6 ) Write the fractional eponent as we have at left to help you break down what is going on here. You can do this with any fractional eponent because an eponent raised to another eponent just means that you multiply the eponents together. In this case,. 2 2 ( 6 ) For fractional eponents, you need to remember that when you see an eponent of it is equivalent to a square root. Similarly: 4 4 And so on ( 4 ) We know that 6 4 so we insert that result here. 64 Since , this is the answer. Ans: 64 Page

13 Section Fractional Eponents 6) Simplify the epression: 52 4 ( 4 ) 5 Write the fractional eponent as we have at left to help you break down what is going on here. You can do this with any fractional eponent because an eponent raised to another eponent just means that you multiply the eponents together. In this case, ( 4 ) 5 For fractional eponents, you need to remember that when you see an eponent of it is equivalent to a square root. Similarly: 4 4 And so on ( 2 ) 5 We know that 4 2so we insert that result here. 2 Since , this is the answer. Ans: 2 Page

14 Section Fractional Eponents 7) Simplify the epression: 2 27 ( 27 ) 2 Write the fractional eponent as we have at left to help you break down what is going on here. You can do this with any fractional eponent because an eponent raised to another eponent just means that you multiply the eponents together. In this case, 2 2. ( ) 2 27 For fractional eponents, you need to remember that when you see an eponent of it is equivalent to a square root. Similarly: 4 4 And so on (continued on net page) Page 4

15 Section Fractional Eponents 27 We write our factor tree to simplify the cubed root and look for triplets of numbers. The factor tree tells us that 27 ( ) 2 9 Since 27 we replace the cubed root in our problem with. Perform the squaring operation. Ans: 9 Page 5

16 Section Fractional Eponents 8) Simplify the epression: 47 7 ( )( ) Since you are multiplying two eponents with the same base, you just add the eponents together. 77 Add the eponents Simplify the 7/7 in the eponent. Since, we cannot simplify this any further. Ans: Page 6

17 Section Fractional Eponents 9) Simplify the epression: ( 8 ) Since we are raising an eponent to another 8 eponent, we just multiply the eponents together. 8 Multiply the eponents 8 Simplify the / in the eponent. 8 Since, we cannot simplify this any further. Ans: 8 Page 7

18 Section Fractional Eponents 0) Simplify the epression: 8 ( ) 8 Since we are raising an eponent to another 8 8 eponent, we just multiply the eponents together. Multiply the eponents Simplify the / in the eponent. 27 Since 27, we cannot simplify this any further. Ans: 27 Page 8

19 Section Fractional Eponents ) Simplify the epression: 9/7 2/7 another eponent, and both have the same base, we just subtract the eponents. Since we are dividing an eponent by Finalize the eponent subtraction. Simplify the fraction in the eponent. Since, we cannot simplify this any further. Ans: Page 9

20 Section Fractional Eponents ) Simplify the epression: /5 8/5 another eponent, and both have the same base, we just subtract the eponents. Since we are dividing an eponent by Subtract the eponents 27 Simplify the fraction in the eponent. 27 The / eponent is equivalent to a cubed root. Since 27, we note that 27 and we cannot simplify this any further. Ans: Page 20

21 Section Fractional Eponents ) Simplify the epression: ( 27 2/ 5 / ) You cannot add the eponents on the inside of the parenthesis because the bases ( and 5) are different. Instead, apply the eponent on the outside of the parenthesis to each term on the inside by multiplying eponents. In other words, you will multiply each eponent on the inside by Do the eponent multiplication. Simplify the fractions in the eponent. Perform the eponent operation for the term with 27 in it. Perform the multiplication. Ans: 645 Page 2

22 Section Fractional Eponents 4) Simplify the epression without using any negative eponents: / 8 8 / 8 You can write any negative eponent as one over the positive eponent. Change the eponent in the bottom to a cubed root. 2 We know that 8 2 because Ans: 2 Page 22

23 Section Fractional Eponents 5) Simplify the epression without using any negative eponents: /2 6 6 /2 ( 6 /2 ) ( 6 ) ( 4) 64 You can write any negative eponent as one over the positive eponent. Rewrite the denominator to make it clearer to see what to do net. Change the eponent in the bottom to a square root. We know that 6 4 so fill that in. In the bottom we see that Ans: 64 Page 2

24 Section Fractional Eponents 6) Simplify the epression without using any negative eponents: 9 ( ) / 9 Multiply the eponents together. 9 Do the eponent multiplication. Simplify the fractional eponent. Ans: Page 24

25 Section Fractional Eponents 7) Simplify the epression without using any negative eponents: ( ) /4 4 Multiply the eponents together. 6 4 Do the eponent multiplication. 9 Simplify the fractional eponent. Ans: 9 Page 25

26 Section Fractional Eponents 8) Simplify the epression without using any negative eponents: 7/6 5/6 5/6 5/6+ 5/6 7/6 0/6 7/6 0/6 7/6 In the numerator, since you are multiplying two terms together that have the same base, just add the eponents. Do the eponent addition in the numerator. Since you are dividing two terms that have the same base, you can subtract the eponents. /6 Carry out the eponent subtraction. /2 Simplify the fractional eponent. Ans: /2 Page 26