Supplemental Worksheet Problems To Accompany: The Algebra ...€¦ · 4. 52. Begin. ()4. 12 5....

$: Supplemental Worksheet Problems To Accompany: The Algebra ...€¦ · 4. 52. Begin. ()4. 12 5. Write the fractional exponent as we have at left to help you break down what is going$
© 2008 Jason Gibson / MathTutorDVD.com The Algebra 2 Tutor Section 13 – Fractional Exponents

Supplemental Worksheet Problems To Accompany:

The Algebra 2 Tutor

Section 13 – Fractional Exponents

Please watch Section 13 of this DVD before working these problems.

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1) Simplify the expression:

1 2100


1 38


1 2964

⎛ ⎞⎜ ⎟⎝ ⎠

Page 2



( )1 3125−


3 216


5 24

Page 3



2 327


( )( )4 7 3 73 3


( )31 38

Page 4



( )83 83


9/7

2/7

1111


13/15

8/15

2727

Page 5



( )32/3 1/327 5⋅

14) Simplify the expression without using any negative exponents:

1/38−


3/216−

Page 6



( )1/39x


( )3/412x


5/6 5/6

7/6

x xx⋅

Page 7


Question

Answer


1 2100

Begin.

100

For fractional exponents, you need to remember that when you see an exponent of 1 2 it is equivalent to a square root . Similarly:

1 2

1 3 3

1 4 4

x x

x x

x x

=

=

=

And so on…

10

We could write a factor tree for 100 , but we know from experience that 100 10= since 10 times 10 equals 100.

Ans: 10

Page 8


Question

Answer


1 38

Begin.

3 8


1 2

1 3 3

1 4 4

x x

x x

x x

=

=

=

And so on…

Write your factor tree to simplify the cubed root and look for triplets of numbers.

3 8 2=

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

83

2 2 2

Page 9


Question

Answer


1 2964

⎛ ⎞⎜ ⎟⎝ ⎠

Begin.

964


1 2

1 3 3

1 4 4

x x

x x

x x

=

=

=

And so on…

964

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.

38

We note in the top that 9 3= and in the bottom 64 8= . This fraction can not be simplified any further.

Ans: 38

Page 10


Question

Answer


( )1 3125−

Begin.

3 125−


1 2

1 3 3

1 4 4

x x

x x

x x

=

=

=

And so on…

Write your factor tree to simplify the cubed root and look for triplets of numbers. Prove to yourself that this is true: ( ) ( ) ( )5 5 5 12− ⋅ − ⋅ − = − 5

3 125 5− = −

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−

3 125−

5− 5− 5−

Page 11


Question

Answer


3 216

Begin.

( )31 216 Write the fractional exponent as we have at left to help you break down what is going on here. You can do this with any fractional exponent because an exponent raised to another exponent just means that you multiply the exponents together.

In this case, 1 3 32 1 2⋅ = .

( )316


1 2

1 3 3

1 4 4

x x

x x

x x

=

=

=

And so on…

( )34

We know that 16 4= so we insert that result here.

64

Since 4 4 4 64⋅ ⋅ = , this is the answer.

Ans: 64

Page 12


Question

Answer


5 24

Begin.


In this case, 1 5 52 1 2⋅ = .

( )54


1 2

1 3 3

1 4 4

x x

x x

x x

=

=

=

And so on…

( )52

We know that 4 2= so we insert that result here.

32

Since 2 2 2 2 2 32⋅ ⋅ ⋅ ⋅ = , this is the answer.

Ans: 32

Page 13


Question

Answer


2 327

Begin.


In this case, 1 2 23 1 3⋅ = .

( )23 27


1 2

1 3 3

1 4 4

x x

x x

x x

=

=

=

And so on… (continued on next page)

Page 14


We write our factor tree to simplify the cubed root and look for triplets of numbers. The factor tree tells us that 3 27 3=

( )23

Since 3 27 3= we replace the cubed root in our problem with ‘3’.

9

Perform the squaring operation.

Ans: 9

3 27

3 3 3

Page 15


Question

Answer


( )( )4 7 3 73 3

Begin.

4 7 3 73 +

Since you are multiplying two exponents with the same base, you just add the exponents together.

7 73

Add the exponents

13

Simplify the ‘7/7’ in the exponent.

3

Since 13 3= , we cannot simplify this any further.

Ans: 3

Page 16


Question

Answer


( )31 38

Begin.

1 33 18⋅

Since we are raising an exponent to another exponent, we just multiply the exponents together.

3

38

Multiply the exponents

18


8

Since 13 3= , we cannot simplify this any further.

Ans: 8

Page 17


Question

Answer


( )83 83

Begin.

3 88 13⋅

Since we are raising an exponent to another exponent, we just multiply the exponents together.

313

Multiply the exponents

33


27

Since 33 3 3 3 27= ⋅ ⋅ = , we cannot simplify this any further.

Ans: 27

Page 18


Question

Answer


9/7

2/7

1111

Begin.

9 27 711−

Since we are dividing an exponent by another exponent, and both have the same base, we just subtract the exponents.

7711

Finalize the exponent subtraction.

111

Simplify the fraction in the exponent. Since 111 11= , we cannot simplify this any further.

Ans: 11

Page 19


Question

Answer


13/15

8/15

2727

Begin.

13 815 1527

−

Since we are dividing an exponent by another exponent, and both have the same base, we just subtract the exponents.

5

1527

Subtract the exponents

1327

Simplify the fraction in the exponent.

3 27

The 1/3 exponent is equivalent to a cubed root.

3

Since 3 3 3 27⋅ ⋅ = , we note that 3 27 3= and we cannot simplify this any further.

Ans: 3

Page 20


Question

Answer


( )32/3 1/327 5⋅

Begin.

2 3 1 33 1 3 127 5⋅ ⋅⋅

You cannot add the exponents on the inside of the parenthesis because the bases (3 and 5) are different. Instead, apply the exponent on the outside of the parenthesis to each term on the inside by multiplying exponents. In other words, you will multiply each exponent on the inside by 3.

6 33 327 5⋅

Do the exponent multiplication.

2 127 5⋅

Simplify the fractions in the exponent.

729 5⋅

Perform the exponent operation for the term with 27 in it.

3645

Perform the multiplication.

Ans: 3645

Page 21


Question

Answer


1/38−

Begin.

1/3

18

You can write any negative exponent as “one over the positive exponent”.

3

18

Change the exponent in the bottom to a cubed root.

12

We know that 3 8 2= because 2 2 2 8⋅ ⋅ =

Ans: 12

Page 22


Question

Answer


3/216−

Begin.

3/2

116

You can write any negative exponent as “one over the positive exponent”.

( )31/2

1

16

Rewrite the denominator to make it clearer to see what to do next.

( )31

16

Change the exponent in the bottom to a square root.

( )314

We know that 16 4= so fill that in.

164

In the bottom we see that 4 4 4 64⋅ ⋅ =

Ans: 164

Page 23


Question

Answer


( )1/39x

Begin.

9 11 3x⋅

Multiply the exponents together.

93x


3x

Simplify the fractional exponent.

Ans: 3x

Page 24


Question

Answer


( )3/412x

Begin.

12 31 4x⋅

Multiply the exponents together.

364x


9x


Ans: 9x

Page 25


Question

Answer


5/6 5/6

7/6

x xx⋅

Begin.

5/6 5/6

7/6

xx

+

In the numerator, since you are multiplying two terms together that have the same base, just add the exponents.

10/6

7/6

xx

Do the exponent addition in the numerator.

10/6 7/6x −

Since you are dividing two terms that have the same base, you can subtract the exponents.

3/6x

Carry out the exponent subtraction.

1/2x


Ans: 1/2x

Page 26

Supplemental Worksheet Problems To Accompany: The Algebra ...€¦ · 4. 52. Begin. ()4. 12 5....

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