Download Found. Math 10 Exponent Practice Test Name: Part A. GCF and

Found. Math 10
Exponent Practice Test
Name:____________________
Part A. GCF and LCM (a& b without a calculator)
1.
Determine the GCF of the following set of numbers.
a) 16 and 64
2.
b) 81 and 108
c) 144, 60 and 54
Determine the LCM of the following set of numbers.
a) 18 and 27
b) 125 and 15
c) 56, 20 and 28
3.
a) Determine the prime factorization of 450.
b) What are the prime factors of 450?
4.
What is the side length of the smallest square that could be tiled with rectangles that measure 20 cm and 44
cm? Assume the rectangles cannot be cut. Sketch the square and rectangles.
Found. Math 10
5.
Exponent Practice Test
Name:____________________
What is the side length of the largest square that could be used to tile a rectangle that measure 20 cm by 44
cm? Assume the squares cannot be cut. Sketch the rectangle and squares.
6. Lukas has 30 pencils, 48 pens and 36 erasers. She wants to package them in containers so that each
container has the same number of each item.
a)
If she wants each container to have the greatest number of items, how many containers will she need?
b)
How many of each item will be in each container?
Part B: Square and Cube Roots – Non-Calculator Section!!
1. Which of the following numbers are perfect squares, perfect cubes, or both? (without a calculator,
Factorize!)
a) 81
2.
b) 64
c) 125
d) 121
e) 729
f) 196
A cube has a volume of 216 cm3. Determine the length of one of the sides, in cm
3. Mr. Comeau wants to build a fence around his garden to prevent the rabbits from eating all the vegetables.
The fencing costs $16 per metre. How much will it cost to enclose a square garden with an area of 144 m2?
4.
Estimate the value of the following radicals to the nearest tenth of a decimal place. Show your work.
a)
50 
b)
3
18
Found. Math 10
Exponent Practice Test
Name:____________________
5. Arrange the radicals in order from least to greatest, without the use of a calculator. Show your work as you
estimate the values of the radicals.
5 2 , 4 3 , 2 3 2 , 33 1
Part C: Real Numbers
Place a check in the box(es) which represent each real number
Question
Natural
Whole
Integer
 5
3
Rational
Irrational
Real
3
0
16
49
2.136 413
641...
Part D: Radicals
1.
Rewrite the following as mixed radicals
a) 96 
e)
2.
24x 5 y 3 
b)
f)
24 
3
c)
180 
d)
64a 5b 4 
Rewrite the following as an entire radical.
a) 4 5 
b) 33 5 
c)  23 6
3
80 
Found. Math 10
Exponent Practice Test
Name:____________________
Part E: Evaluate Exponents
1. Write each as a single power with positive exponents.
x  
a)
2.
b) a
a
4 2
c)
 2.56
 2.53


c


3.8
2.5
f)


8  
 1.2 
4 
2
3

Evaluate the following expressions accurately to two decimals places.
a)
1.6  
2 3
2
b)
2
 2
d) 125  


e)
4.5 
2 1.2 
3
2
3
2.3
3 
2
 34 
3  
 

2


 


4
3
3. The growth of a certain caribou population can be modeled by the formula, P  14001.05 , where P is
the estimated caribou population and n is the number of years. How many caribou are there in 4 years?
n
4.
Evaluate the following expressions without the use of a calculator.

a)

0.25
3
2
b)
 25 
 
 16 
1
2

c)
8
 
 27 
2
3

Found. Math 10
Exponent Practice Test

d) 49  

1

 64 
5.
a)

1
2
e)

2
3
Name:____________________

 1  
   81
 64 
1
2
f)
Evaluate, with the aid of a calculator , if needed.
2
1
4 4 
b)
1
1
 3 
2
5
3
 25 
100   
4
1
2
1
2

 3  2  
 2  3 
c)
2
5
3
1
Part F: Exponent Laws
1.
Caleb simplified
 64x  . Here are his steps:
4
2
3
2
3
8
3
Step 1:
64 x
Step 2:
 
Step 3:
83 x 3
3
8
64 x 3
8
8
512x 3
Step 4:
In which step did he make a mistake, if any?
If he made a mistake, show the correct solution.
2.
Simplify the following expressions.
1
3
2 2
2


 72 x y 

b) 
3 
 2 x 4 y 


2
a)
6x y
3x y
c)
 27a b 
3
4

2
2
9 3


5
2
7x y

d) 
2
3

 2 x 2

y  
8

Found. Math 10
Exponent Practice Test
2
e)
100a b
25a b

2
2
3
1
3
4 2
5
 4 1
8
3

 20 x y
i) 
5
 5x y

k)
y 4
y


 100a 
f) 
1 
2


 25a b 2 



g)  2m n
3m n 
Name:____________________
3


h) 

9m
5
3

1
2

7
 

 4m 2  


3
2

 


j)

l)
 x  x  
3
4
y
7
5
m) Write as a single power
 
6
4 3
x
3
5
y
4
y
2
