Order of Operations, Exponents, and Powers of Ten Test
Review (Answers in red)
Please Note: 10^5=10 5
1. James bought 8 books for $6 each and 5 notebooks
for $3 each. Write an expression to show how much he
spent. Solve the expression.
Since James bought 8 books for $6 each, we can
multiply them and get 8x6 for book part of the
expression. We can also multiply $5x3 to get the
notebook part. So the expression is:
6. Insert parenthesis to make the number sentence
true. 15 ÷ 3+4+5=14 It doesn’t need any!
7. Use the correct order of operations to simplify.
4 x (33+2)
4x(27+2) (because 3^3 = 3x3x3=9x3=27)
4x(29)=116
8. According to the order of operations, do you multiply
or divide first? Depends on which comes first from leftto-right
8x6 + 5x3
48 + 15 = 63
2. Insert parenthesis to make this number sentence
2
true. 81+19 ÷ 5 +5= 9
(81+19) ÷ 5 2 +5= 9
3. Use the order of operations to simplify. 10 5 -4+1
9. What should you do first in the following problem?
8x2+2 4 Evaluate the exponent (2^4=64)
10. What operation should you do last in the following
problem? 19+45 ÷ 3-11 subtraction, because it is to the
right between addition and subtraction
10 5 -4+1
11. JoBeth said that the value of 8 x 3 ÷ 4 x 2 ÷5 = 42.
Is she correct? Explain why you think so.
100,000-4+1 (since 10^5 = 100,000)
No, because: 8 x 3 ÷ 4 x 2 ÷5
99,996+1 (since 100,000-4=99,996)
=24 ÷ 4 x 2 ÷5 (because 8x3=24)
=99,997
=6x 2 ÷5
4. Use the order of operations to simplify.
=12÷5
15-18 ÷ 9+3 0
15-18 ÷ 9+3 0
=2.4 Which is not 42!
12. What is the value of 100? 1 (look at your notes for
this)
15-18 ÷ 9 + 1 (since 3^0 = 1)
15-2+1 (since 18 divided by 9 =2)
13+1=14
5. What is the correct order of operations?
Parenthesis, Exponents, Multiplication and division
from left-to-right, addition and subtraction from left-toright
13. The distance between Rock Hill and Austin, Texas is
1000 miles. Write this as a power of 10. 10^3
14. Every year many students begin middle school. In
the U.S. approximately 105 students began middle
school this year. Write 105 in standard form. 100,000
15. Elephants are native to Africa. At one time,
elephants were in danger of becoming extinct. Now the
estimated population of elephants is 10,000,000,000.
Write this as a power of ten. 10^10
Order of Operations, Exponents, and Powers of Ten Test
Review (Answers in red)
16. Write the following using a power of ten.
10 x 10 x 10 x 10 x 10 = 10^5
17. Alex read 105 pages. Lucy read 103 pages. How
many more pages did Alex read than Lucy?
105 = 100,000
103=1000, so 100,000-1000=99,000
18. What is another way to write 10,000?
10^4
19. Write a number equal to 101 + 103 + 105.
101=10, 103=1000, 105=100,000
20. Cody bought 100 pieces of bubble gum. Caleb buys
one hundred times as many pieces as him. How many
pieces did Caleb buy? Write you answer as a power of
ten. 100x100 = 10,000, which is 10^4
21. Explain how you would solve 32-4x2+10.
First, multiply 4x2 to get 8. Then subtract 32-8 to get 24,
then add 24+10 to get 34.
22. Explain how to solve 54 ÷ 3 2 -3x2.
First, evaluate 3 2 which is 9. Then 54 ÷ 9 which is 6.
Then multiply 3x2 which is 6. Then subtract 6-6 to get 0.
23. Solve: 4 3 64
24. Solve: 9 3 729
25. Solve 35 243
26. Solve: 82 64
Write in exponential form:
26. 125 5 3
27. 9 3 2
28. 27
33
29. 8 2 4