Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 8 Powers and Exponents

Transcription

1 Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Please watch Section 8 of this DVD before working these problems. The DVD is located at: Page 1

2 Part 1: Writing Product of Terms as Exponents 1) Express the following as an exponent: 2) Express the following as an exponent: 3) Express the following as an exponent: 4) Express the following as an exponent: 5) Express the following as an exponent: 6) Express the following as an exponent: Page 2

3 Part 2: Writing Exponents as a Product of Terms 7) Express the following as a product of terms. 8) Express the following as a product of terms. 9) Express the following as a product of terms. 10) Express the following as a product of terms. 11) Express the following as a product of terms. 12) Express the following as a product of terms. 13) Express the following as a product of terms. Page 3

4 Part 3: Multiplying Exponents 14) Simplify the following: 15) Simplify the following: 16) Simplify the following: 17) Simplify the following: 18) Simplify the following: 19) Simplify the following: 20) Simplify the following: Page 4

5 Part 4: Dividing Exponents 21) Simplify the following: 22) Simplify the following: 23) Simplify the following: 24) Simplify the following: 25) Simplify the following: 26) Simplify the following: 27) Simplify the following: Page 5

6 Part 5: Evaluate and simplify the following expressions 28) 29) 30) 31) 32) 33) 34) 35) Page 6

7 Question Answer 1) Express the following as an exponent: Begin First we identify our base which is the number we are multiplying against itself. In this case our base is the number 5. We then count how many times we are multiplying the base against itself by simply counting how many times the base is repeated which in this case is 4. This is our exponent. We then use this information to write out our exponent expression. Page 7

8 2) Express the following as an exponent: Begin First we identify our base which is the number we are multiplying against itself. In this case our base is the number 11. We then count how many times we are multiplying the base against itself by simply counting how many times the base is repeated which in this case is 3. This is our exponent. We then use this information to write out our exponent expression. Page 8

9 3) Express the following as an exponent: Begin First we identify our base which is the number we are multiplying against itself. In this case we see there are two numbers or variables we are multiplying so we will end up with two bases, x and y. We then count how many times we are multiplying the base against itself by simply counting how many times the base is repeated which in this case is 5 for x and 2 for y. This is our exponent for each variable. We then use this information to write out our exponent expression. Since we can t combine the bases we end up with a product of exponents. Page 9

10 4) Express the following as an exponent: Begin First we identify our base which is the number we are multiplying against itself. In this case our base is the number -3. We know it s -3 and not simply 3 since the negative sign gets repeated each time we write the base. We then count how many times we are multiplying the base against itself by simply counting how many times the base is repeated which in this case is 4. This is our exponent. We then use this information to write out our exponent expression. Page 10

11 5) Express the following as an exponent: Begin First we identify our base which is the number we are multiplying against itself. In this case we see there are two numbers or variables we are multiplying so we will end up with two bases, 10 and d. We then count how many times we are multiplying the base against itself by simply counting how many times the base is repeated which in this case is 1 for 10 and 3 for d. This is our exponent for each variable. We then use this information to write out our exponent expression. Since we can t combine the bases we end up with a product of exponents. Page 11

12 6) Express the following as an exponent: Begin First we identify our base which is the number we are multiplying against itself. In this case we see there are two numbers or variables we are multiplying so we will end up with two bases, 7 and 8. We then count how many times we are multiplying the base against itself by simply counting how many times the base is repeated which in this case is 2 for 7 and 3 for 8. This is our exponent for each variable. We then use this information to write out our exponent expression. Since we can t combine the bases we end up with a product of exponents. The negative sign just stays out in front of our answer. Page 12

13 7) Express the following as a product of terms. Begin First we identify our base which is the number we are multiplying against itself. In this case our base is the number 2. We then find out how many times we are going to multiply the base against itself or how many times we are going to write out our base. The exponent gives us this information which in this case is 4. We then use this information to write out our product of terms. Page 13

14 8) Express the following as a product of terms. Begin First we identify our base which is the number we are multiplying against itself. In this case our base is the number -a. We then find out how many times we are going to multiply the base against itself or how many times we are going to write out our base. The exponent gives us this information which in this case is 3. We then use this information to write out our product of terms. Page 14

15 9) Express the following as a product of terms. Begin First we identify our base which is the number we are multiplying against itself. In this case we notice two bases, 5 and y. We then find out how many times we are going to multiply the base against itself or how many times we are going to write out our base. The exponent gives us this information which in this case is 1 for the base 5 and 5 for the base y. We then use this information to write out our product of terms. Page 15

16 10) Express the following as a product of terms. Begin First we identify our base which is the number we are multiplying against itself. In this case we notice two bases, -2 and 12. We then find out how many times we are going to multiply the base against itself or how many times we are going to write out our base. The exponent gives us this information which in this case is 2 for the base -2 and 4 for the base 12. We then use this information to write out our product of terms. Page 16

17 11) Express the following as a product of terms. Begin First we identify our base which is the number we are multiplying against itself. In this case our base is the number 1. We then find out how many times we are going to multiply the base against itself or how many times we are going to write out our base. The exponent gives us this information which in this case is 6. We then use this information to write out our product of terms. Page 17

18 12) Express the following as a product of terms. Begin First we identify our base which is the number we are multiplying against itself. In this case we notice two bases, x and y. We then find out how many times we are going to multiply the base against itself or how many times we are going to write out our base. The exponent gives us this information which in this case is 4 for the base x and 2 for the base y. We then use this information to write out our product of terms. Page 18

19 13) Express the following as a product of terms. Begin First we identify our base which is the number we are multiplying against itself. In this case our base is the number 99. We then find out how many times we are going to multiply the base against itself or how many times we are going to write out our base. The exponent gives us this information which in this case is 4. We then use this information to write out our product of terms. Don t forget about the negative sign in front of the expression. Because we don t have any parenthesis here, the negative sign just sits out in front and doesn t participate in the exponent. Page 19

20 14) Simplify the following: Begin When multiplying exponents with the same base, you add the exponents. First we check to see if the base of the expressions we are multiplying are the same. If they are, then we simply add the exponents and rewrite our expression. Page 20

23 17) Simplify the following: Begin When multiplying exponents with the same base, you add the exponents. First we check to see if the base of the expressions we are multiplying are the same. If they are, then we simply add the exponents and rewrite our expression. In this case we notice there are two bases, 9 and z. The only expression we can simplify is the ones with base of 9. Page 23

24 18) Simplify the following: Begin When multiplying exponents with the same base, you add the exponents. Can t Simplify Further First we check to see if the base of the expressions we are multiplying are the same. In this case we notice right away that we have two different exponent expressions with different bases. This means we can t simplify further in a form of an exponent. Can t Simplify Further Page 24

27 21) Simplify the following: Begin When dividing exponents with the same base, you subtract the exponents. First we check to see if the base of the expressions we are dividing are the same. If they are, then we simply subtract the exponent in the denominator from the exponent in the numerator and rewrite our expression. Page 27

30 24) Simplify the following: Begin When dividing exponents with the same base, you subtract the exponents. First we check to see if the base of the expressions we are dividing are the same. If they are, then we simply subtract the exponent in the denominator from the exponent in the numerator and rewrite our expression. Remember that anything to the power of 1 equals the base itself. Page 30

32 26) Simplify the following: Begin When dividing exponents with the same base, you subtract the exponents. First we check to see if the base of the expressions we are dividing are the same. If they are, then we simply subtract the exponent in the denominator from the exponent in the numerator and rewrite our expression. We notice that in this case our exponent result is zero, which means we end up with 1. Remember that anything to the power of zero will always equal 1. Page 32

34 28) Begin First, let s evaluate the expression by substituting the values expressed by the letters. When multiplying exponents with the same base, you add the exponents. Next we notice we are multiplying two exponents with the same base, so we simply add the exponents and rewrite our exponent expression. Page 34

35 29) Begin First, let s evaluate the expression by substituting the values expressed by the letters. When multiplying exponents with the same base, you add the exponents. Next we notice we are multiplying two exponents with the same base, so we simply add the exponents and rewrite our exponent expression. Remember that any number by itself can be rewritten as that number to the power of 1. Page 35

36 30) Begin First, let s evaluate the expression by substituting the values expressed by the letters. When multiplying exponents with the same base, you add the exponents. Next, we notice that the base of the two numbers we are multiplying are not equal. However, we know that 25 is a product of 5 squared so we can rewrite 25 in that manner since they are equal to the same thing. We now have a common base so we can simplify. Page 36

37 31) Begin First, let s evaluate the expression by substituting the values expressed by the letters. When dividing exponents with the same base, you subtract the exponents. First we check to see if the base of the expressions we are dividing are the same. If they are, then we simply subtract the exponent in the denominator from the exponent in the numerator and rewrite our expression. Page 37

38 32) Begin First, let s evaluate the expression by substituting the values expressed by the letters. When dividing exponents with the same base, you subtract the exponents. First we check to see if the base of the expressions we are dividing are the same. If they are, then we simply subtract the exponent in the denominator from the exponent in the numerator and rewrite our expression. Remember that anything to the power of 1 equals the base itself. Page 38

39 34) Begin First, let s evaluate the expression by substituting the values expressed by the letters. When dividing exponents with the same base, you subtract the exponents. Can t simplify further First we check to see if the base of the expressions we are dividing are the same. In this case we notice right away that we have two different exponent expressions with different bases. This means we can t simplify further in a form of an exponent. Can t Simplify Further Page 39

40 35) Begin First, let s evaluate the expression by substituting the values expressed by the letters. When multiplying exponents with the same base, you add the exponents. First we check to see if the base of the expressions we are multiplying are the same. If they are, then we simply add the exponents and rewrite our expression. Page 40