a)
7

2(3
2
)
b)
(

4

3)
2
+
(

3)
2
c)
(

2)
6
÷
4
3
d)
24

2
2
+
(7
2

5
2
)
Apply
10.
For each pair of expressions, which one has
a greater value? How much greater is it?
a)
3(2)
3
2(3)
2
b)
(3
×
4)
2
3
2
×
4
2
c)
6
3
+
6
3
(6
+
6)
3
11.
Find the step where Justin made an error.
Show the correct answer.
(3 + 6)
2
 4 × 3
2
= 3
2
 4 × 3
2
Step 1
= 9  4 × 9
Step 2
= 5 × 9
Step 3
= 45
Step 4
12.Find the step where Katarina made an error. What is the correct answer?
2
= 32 ÷ (8) + 5 × 8
Step 1
= 4 + 5 × 8
Step 2
= 4 + 40
Step 3
= 36
Step 4
13.Write an expression with powers to determine the difference between the volume of the small cube and the volume of the large cube. What is the difference?
14.
Read the following riddle and then answer
the questions below.
In downtown Victoria, there are seven pink
houses. Every pink house has seven pink
rooms, every pink room has seven cats, and
every cat has seven kittens.
a)
How many pink rooms are there?
b)
How many kittens are there?
c)
Write an expression using powers of 7
to determine the total number of houses,
rooms, cats, and kittens. Evaluate your
expression.
15.Write an expression with powers to determine the difference between the area of the large square and the area of the small square. What is the difference?
16.A red square with a side length of 8 cm is placed on a yellow square with a side length of 10 cm. Write an expression with powers to determine the visible yellow area. What is the visible yellow area?
17.What is the value of 532?
18.
In a game show called The Pyramid of
Money, a contestant must successfully
answer a set of questions. The first question
is worth $3125. Each question after that is
worth four times the value of the previous
question.
a)
What is the value of question 2? question
3? question 4?
b)
How many questions would a contestant
have to answer correctly before becoming
eligible to answer a question with a value
of $3 200 000?
c)
Which question is represented by the
expression 3125
×
4
7
?
d)
Write an expression with powers that
represents the sum of the values of the
first four questions.
19.
A phone tree is used to notify the players on
a football team about a change in the time
for their next game. Each of the three
coaches calls two different players, and then
each player calls two more players. Each
person only makes two calls. The chart
shows the number of people calling and
receiving calls for each round of two calls.
Round
of
Calls
Number
of People
Calling
Number
of Calls
Received
Total Number
of People
Notified
First
3
6
3
+
6
=
9
Second
6
12
9
+
12
=
21
Third
12
24
21
+
24
=
45
Fourth
24
45
+
=
93
a)
What value belongs in each unknown
box?
b)
Write an expression for the number from
part a) as a product of 3 and a power
of 2.
c)
What does the 3 in part b) represent?
d)
What does the exponent in part b)
represent?
e)
Imagine that the phoning continued.
Determine an expression for the number
of calls received in the sixth round and
evaluate it.
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 Fall '14
 Exponential Function, Power, Alice in Wonderland, Orders of magnitude, Exponentiation, Power of two