Exponents and Prime Factorization
Write this expression as a power
8×8×8×8×8×8×8
87
Find the LCM of 4 and 9.
36
Write an expression for this situation:
A number of eggs, e, divided by 12
e / 12
Evaluate this expression when x=4
12x-7
41
Simplify this expression:
9y + 4 - 6y
3y + 4
Evaluate this exponent: 34
81
Find the GCF of 30 and 100.
10
Write an expression for this situation:
3 times the sum of m and 7
3(m + 7)
*TEST QUESTION* Evaluate the expression 8.952+p for p=0.276.
9.228
Simplify this expression:
8x + 13 - 3x + 9
5x + 22
Find the prime factorization of each number
a. 50
b. 36
c. 72
a. 2 x 5 x 5 or 2 x 52
b. 2 x 2 x 3 x 3 or 22 x 32
c. 2 x 2 x 2 x 3 x 3 or 23 x 32
Find the GCF and LCM of 8 and 12.
GCF: 4
LCM: 24
Write an expression for this situation:
22 less than 5 times a number f
5f - 22
Evaluate this expression when z=1 and n=7
5z + 3n - z3
25
Make an equivalent expression for each one:
a. 2(x + 4)
b. 5x - 45
a. 2x + 8
b. 5(x - 9)
Zoe wrote the prime factorization of 40. Which expressions could she have written? Select all that apply.
A. 4×10
B. 2×2×10
C. 2×2×2×5
D. 24
E. 23×5
C and E
*TEST QUESTION* For questions a - d, choose Yes or No to tell whether 5 is the GCF of the pair of numbers.
a. 15 and 25
b. 40 and 70
c. 45 and 60
d. 65 and 75
a. yes
b. no
c. no
d. yes
*TEST QUESTION* Water bottles are sold in cases of 24. Select the expressions that can represent the total number of water bottles in c cases.
A. 24 x c
B. 24/c (divided by)
C. 24 + c
D. 24 - c
E. 24c
A and E
*TEST QUESTION* Evaluate the expression below.
(5.2+6.3)- 12 / 2.5
(That's 12 divided by 2.5)
6.7
*TEST QUESTION* For questions a–d, choose Yes or No to tell whether the expressions are equivalent.
a. 6a + 12 and 3(3a + 4)
b. 3(5b - 2) and 8b - 5
c. 5(5c + 6) and 25 + 30c
d. 20d - 16 and 4(5d - 4)
a. No
b. No
c. No
d. Yes
*TEST QUESTION* The same digits are used for the expressions 52 and 25. Explain how these are different and solve both.
52 is 5 x 5 = 25
25 is 2 x 2 x 2 x 2 x 2 = 32
They are different because the base is the number you multiply and they have a different base, so you are multiplying different numbers.
*TEST QUESTION* At her health club, Lauren uses a treadmill every 2 days and the weight machines every 8 days. She used a treadmill on March 2 and will use the weight machines on March 8. Lauren says that the first time she will use both a treadmill and the weight machines in March is March 16 because the LCM of 2 and 8 is 16. Does Lauren’s reasoning make sense? Why or why not?
No; Sample answer: Lauren’s reasoning does not make sense. The LCM is 8, not 16. So, March 8 will be the first time she uses both a treadmill and the weight machines.
*TEST QUESTION* Ms. Perkins wants to rent a car for a day. It will cost the daily fee of $75 plus $0.55 per mile driven.
A. Let m= the number of miles Ms.Perkins drives for the day. Write an expression that shows the amount she will pay for the car.
B. Evaluate the expression you wrote to find the amount Ms. Perkins will pay if she drives 300 miles.
A. 75 + 0.55m
B. $240
*TEST QUESTION* Select each expression that has a value of 24 when x=18.
a. 5,760 / x
b. x/6 + 21
c. 162/x + 17
d. 2x2 / 27
e. (4,050 / x) - 201
B, D, and E
Select the expressions that are equivalent to 18m-12.
a. 6m - 4 + 6m - 4 + 6m - 4
b. 12m + 6 - 6m - 6
c. 6(3m-2)
d. 3(6m-4)
e. 24n - 42 + 8 - 6m
A, C, D