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© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 1
Supplemental Worksheet Problems To Accompany:
The Pre-Algebra Tutor: Volume 1
Section 8 – Powers and Exponents
Please watch Section 8 of this DVD before working these problems.
The DVD is located at:
http://www.mathtutordvd.com/products/item66.cfm
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 6
Part 5: Evaluate and simplify the following expressions
28)
29)
30)
31)
32)
33)
34)
35)
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 21
15) 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 22
16) 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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. Ans: Can’t Simplify Further
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 25
19) 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 26
20) 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 28
22) 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 29
23) 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 31
25) 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 33
27) 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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. Ans: Can’t Simplify Further
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents
Page 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.
Ans:
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