IntrotoRationalExpressions&–&Fractions&andExponents&Review ...

Intro to Rational Expressions ? Fractions and Exponents Review ? Worksheet

MCR3U Jensen

1) Add or subtract the following fractions.

a) 2 + 3

b) 3 - 1

c) x + y

d) 3x - 2 y

34

53

32

57

2) Simplify (multiplication)

a)

2 3

-

1 5

b)

4 5

25 12

c)

17 8

13 289

d)

-

5 8

75 128

3) Simplify (multiplication and division)

a)

d) ?

b) --!! --!

!!

e)

! c)

?

4) Simplify (exponents)

a) (x6)(x4)

b) (y3)(y7)(y9)

e) h6 ? h8

x10

f )

x5

( ) ( ) i)

x2

3

y3

2

j) (-x)2

(-x)

5) Simplify fractions and exponents

a)

c) m5 ? m4

d) h6 ? h8

( ) g)

yz 2

3

h)

-

(

x

)2

2

b)

6) Simplify. Your answer should contain only positive exponents.

a) !!!! !

b) ! !! 2!

d) 2 ! 2!

e) !! ! !!!!!!!! !! !! ! !!

g) !!!!!!!!!

h) !!!!!!!!!!!!!

j)

!!!! !!!!

!

c)

! ! 2!! f) !!!!!!!!!!!!

i)

! !!!

!

Answers

1. a) 17

12

b) 4

c) 2x + 3y

15

6

d) 21x - 10 y

35

2. a) - 2

15

b) 5

c) 13

d ) - 25 3

3

8

64 2

3. a) (7/9)

b) (77/20)

c) (--34/45)

d) (36/49)

e) 14

4. a) x10

b) y19 c) m d)

e) 1/h

f ) x5

g) y3z6

h) x4

i) x6y6

5. a) !"!!"!

b) !"!

!"!

!

6) a) !!!"

b) !!!

c) 2!

d) 8

!

e) 8

!

!

f) !!!

g) !

!

!!!

h) !!"

i) !

j) !!

!

!

!

!

j) -x

3.3 Rational Exponents ? Worksheet

MCR3U Jensen

1) Evaluate each cube root.

a) ! 64

!

b) -1000 !

!

c)

!

!

2) Evaluate each root.

!

a) 81!

b) ! !"

!

c) 64!

!"#

3) Evaluate.

!

!

!

a) 8!

b) 32!

c) -64 !

4) Evaluate.

a) 16!!!

b) 25!!!

d) - !

!!

!

e)

!" !!!

!!

!

!"

!"

!

d) ! !

!"

d) ! -100 000

!

d) ! !

!" !!!

c) ! !!!

!

f) - !

!!

!

!"

5) Simplify. Express your answers using only positive exponents.

!!

!

!

a) ! !

b) ! !

!

d) !!!!!

!!

e) !

!!!!

6) Simplify. Express your answers using only positive exponents.

!

a) !

?

!!!

b) !!!!!

!!

d)

!!

!

!!!

e)

8

! !

27

!!!

!

c) !!!

!!

! ! !!

f) !!

! !!

c) !

f) 5

7

!!

!

!!

7) The surface area, S, of a sphere can be expressed in terms of its volume, V, using the formula

!

!

= 4 ! 3 !. A beach ball has a volume of 24 000 cm3. Find its surface area, to the nearest hundred

square centimeters.

Answers

2.1/2.2 Multiplying and Dividing Rational Expressions ? Worksheet

MCR3U

Jensen

1) State the restrictions for each function.

a)

b)

c)

d)

2) Simplify each expression and state all restrictions on .

a)

!

!!!!!"!!!!"

b) !!!!!!!!!!!!!""

c) !!!!!!!!!!"

3) Simplify and state the restrictions on the variables.

a) !"! ? !"!!

!!! !!

b) !"!!

!!

?

!!""!!!

c) !!

!!

?

!"!!! !

d) !"!"

!!

?

!!"!"!!!! !

4) Simplify and state the restrictions on the variable.

a) !" ? !!!"

b) !!! ? !!!

!!!" !

!!! !!!

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