h - Pre-Algebra Vol1 Worksheet 8 Powers and · PDF fileQuestion Answer 1) Express the following as an exponent: Begin ... Microsoft Word - h - Pre-Algebra_Vol1_Worksheet_8_Powers and

© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 8 – Powers and Exponents

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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


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Part 1: Writing Product of Terms as Exponents

1) Express the following as an exponent:







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Part 2: Writing Exponents as a Product of Terms

7) Express the following as a product of terms.








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Part 3: Multiplying Exponents

14) Simplify the following:








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Part 4: Dividing Exponents









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Part 5: Evaluate and simplify the following expressions

28)

29)

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Question

Answer


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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.

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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.

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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.

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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.

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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.

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Page 12


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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.

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Page 13


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.

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Page 14


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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.

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Page 15


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.

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Page 16


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.

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Page 17


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.

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Page 18


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.

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Page 19


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.

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Page 20


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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.

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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.

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Page 24


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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


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Page 27


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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.

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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.

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Page 32


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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.

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Page 34

28)

Begin

First, let’s evaluate the expression by substituting the values expressed by the letters.


Next we notice we are multiplying two exponents with the same base, so we simply add the exponents and rewrite our exponent expression.

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Page 35

29)

Begin



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.

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Page 36

30)

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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.

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32)

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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.

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34)

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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


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h - Pre-Algebra Vol1 Worksheet 8 Powers and · PDF fileQuestion Answer 1) Express the following as an exponent: Begin ... Microsoft Word - h - Pre-Algebra_Vol1_Worksheet_8_Powers and