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Powers and Exponents Word Problems
Problem Solving Strategies
Triple Dan, the dragonfly is growing fast. His body length is tripling every month. At the
beginning of his life his length is 1 cm.
a) What is the body length five months into his life?
b) After how many months is his body length more than 700 cm?
What is the surface area of a cube with an edge length of 4 cm?
Name:______________________ Class:______________
A circle is inscribed in a square with a side length of 20 cm. What is the area of the
shaded region?
A circle is inscribed in a square with an area of 100cm2. What is the area of the
unshaded region?
Find the area of the square attached to the hypotenuse.
Find the length of the hypotenuse.
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Find the length of the side b.
Which is larger, the area of a square with a side length of 14 cm or the surface area of a
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cube with an edge length of 6 cm? Write an exponential expression to solve the
problem.
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?
In downtown Victoria, there are seven pink houses. Every pink house has seven pink
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rooms, every pink room has seven pink 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.
A telephone tree is used to send messages. The person at the top calls 2 people. Each
person calls 2 more people.
a) How many people will have been called at the sixth tier?
b) A message is relayed until the bottom row of the tree has 256 people. How
many tiers are there in total?
Name:______________________ Class:______________
In international judo the mat is a square and covers 256 m2. The contest area is also a
square and covers 64 m2. If the contest area is in the center of the mat, what is the
distance from the outer edge of the safety area to the danger area?
The area of a square field is 5476 m2. How much would it cost to put wire fencing
around the field if the cost per meter is $4.25?
***The following question is very difficult. Do not worry if you are unable to solve it.
It will be taken up as a class.
If the number of bacteria doubles in a culture every 15 min and it takes 8 h to produce n
bacteria, how many hours would it take to produce 4n bacteria? How many hours
would it take to produce 32n bacteria?