Exponents
What is the value of:
5^3
A. 15
B. 25
C. 125
D. 625
Correct Answer: C — 125
Solution
5^3=5×5×5
=125
Strategy
The exponent tells how many times the base is used as a factor.
What is the prime factorization of 12?
A. 2×6
B. 3×4
C. 2^2×3
D. 2×3^2
Correct Answer: C
Solution
12=2×6
6=2×3
Therefore:
12=2×2×3
=2^2×3
Strategy
Keep factoring until every factor is prime.
What is:
8+3×4
A. 44
B. 32
C. 20
D. 12
Correct Answer: C — 20
Solution
Multiply first:
3×4=12
Then:
8+12=20
Strategy
Multiplication comes before addition.
What is:
6^2+4
A. 16
B. 36
C. 40
D. 64
Correct Answer: C — 40
Solution
6^2=36
36+4=40
Strategy
Evaluate the exponent before addition.
What is:
5^2−6
A. 13
B. 19
C. 25
D. 31
Double Jeopardy 2
Which is the prime factorization of 120?
A. 2^3×3×5
B. 2^2×3×10
C. 2×60
D. 4×30
Correct Answer: B — 19
Solution
5^2=25
25−6=19
Strategy
Exponent first, subtraction second.
Double Jeopardy 2
Correct Answer: A
Solution
120=12×10
12=2^2×3
10=2×5
Therefore:
120=2^3×3×5
What is the value of:
2^6
A. 12
B. 32
C. 36
D. 64
Correct Answer: D — 64
Solution
2^6=2×2×2×2×2×2
=64
Strategy
Expand the exponent into repeated multiplication.
What is the prime factorization of 20?
A. 2^2×5
B. 2×10
C. 4×5
D. 2×5^2
Correct Answer: A
Solution
20=2×10
10=2×5
Therefore:
20=2^2×5
Strategy
Start with the smallest prime factor, 2, whenever possible.
What is:
(8+3)×4
A. 20
B. 32
C. 44
D. 88
Correct Answer: C — 44
Solution
Parentheses first:
8+3=11
Then:
11×4=44
Strategy
Always solve grouping symbols before other operations.
What is the prime factorization of 30?
A. 2×3×5
B. 3×10
C. 2×15
D. 5×6
Correct Answer: A
Solution
30=2×15
15=3×5
So:
30=2×3×5
Strategy
Make sure every number in your final factorization is prime.
What is:
24÷(4+2)
A. 3
B. 4
C. 8
D. 16
Correct Answer: B — 4
Solution
4+2=6
24÷6=4
Strategy
Parentheses come first.
Which expression has a value of 81?
A. 3^2
B. 3^3
C. 3^4
D. 3^5
Correct Answer: C — 3^4
Solution
3^4=3×3×3×3=81
Strategy
When given the answer, build powers of the base until you reach that number.
What is the prime factorization of 36?
A. 2×18
B. 3×12
C. 2^2×3^2
D. 6^2
Correct Answer: C
Solution
36=6×6
Each 6 can be factored:
6=2×3
So:
36=2×3×2×3
=2^2×3^2
Strategy
After factoring, combine repeated prime factors using exponents.
What is:
7+23
A. 10
B. 15
C. 17
D. 21
Correct Answer: B — 15
Solution
Exponent first:
23=8
Then:
7+8=15
Strategy
Exponents come before addition.
What is:
2^4+18÷3
A. 10
B. 18
C. 22
D. 34
Correct Answer: C — 22
Solution
Exponent:
2^4=16
Division:
18÷3=6
Addition:
16+6=22
Strategy
Complete exponents and division before addition.
What is:
(12−4)÷2+3
A. 4
B. 7
C. 9
D. 11
Correct Answer: B — 7
Solution
12−4=8
8÷2=4
4+3=7
Strategy
Solve one PEMDAS level at a time.
Which expression is equivalent to:
4×4×4×4×4
A. 4^4
B. 4^5
C. 5^4
D. 5^5
Correct Answer: B — 4^5
Solution
There are five factors of 4.
4×4×4×4×4=4^5
Strategy
The repeated number is the base. The number of factors is the exponent.
What is the prime factorization of 72?
A. 2^3×3^2
B. 2^2×3^3
C. 6×12
D. 8×9
Double Jeopardy 1
What is the value of:
4^2+3×5
A. 19
B. 31
C. 47
D. 80
Correct Answer: A
Solution
72=8×9
8=2^3
9=3^2
Therefore:
72=2^3×3^2
Strategy
Factor each composite number completely before writing the final answer.
Double Jeopardy 1
Correct Answer: B
42=16
3×5=15
16+15=31
What is:
5+3^2×2
A. 23
B. 26
C. 32
D. 46
Correct Answer: A — 23
Solution
Exponent:
3^2=9
Multiplication:
9×2=18
Addition:
5+18=23
Strategy
Follow:
Exponents → Multiplication → Addition
Which expression is equivalent to 48?
A. 2^3×3
B. 2^4×3
C. 2^3×6
D. 4^2×3
Correct Answer: B
Solution
2^4=16
16×3=48
Strategy
Evaluate each choice to determine which is equivalent to the target number.
What is:
3^2+(16−4)÷2
A. 11
B. 12
C. 15
D. 21
Correct Answer: C — 15
Solution
Exponent:
3^2=9
Parentheses:
16−4=12
Division:
12÷2=6
Addition:
9+6=15
Strategy
Mark each step as you complete it.
Which statement correctly explains:
3^4
A. 3×4
B. 4×4×4
C. 3+4
D. 3×3×3×3
FINAL JEOPARDY (WORTH 3X THE POINTS)
Which expression is equivalent to:
72
and also represents its prime factorization?
Correct Answer: D
Solution
The base is 3 and the exponent is 4.
3^4=3×3×3×3
Strategy
Remember:
Base = repeated factor
Exponent = number of factors
FINAL JEOPARDY (WORTH 3X THE POINTS)
Correct Answer: 2^3×3^2
Solution
Start with:
72=8×9
Factor each number:
8=23
9=32
Therefore:
72=2^3×3^2
Both 2 and 3 are prime, so this is the prime factorization.
Final Strategy
Ask three questions:
Does the expression equal the original number?
Are all of the factors prime?
Can repeated factors be represented with exponents?
If all three are true, you have the prime factorization.
Which is the prime factorization of 90?
A. 9×10
B. 2×3^2×5
C. 2×45
D. 3×30
Correct Answer: B
Solution
90=9×10
9=3^2
10=2×5
Therefore:
90=2×3^2×5
Strategy
A prime factorization must contain only prime numbers.
What is:
3^2×(8+4)÷6−5
A. 8
B. 13
C. 18
D. 23
Correct Answer: B — 13
Solution
Exponent:
3^2=9
Parentheses:
8+4=12
Now:
9×12÷6−5
Multiplication and division work left to right:
9×12=108
108÷6=18
Then:
18−5=13
Strategy
Use PEMDAS carefully and remember:
Multiplication and division have equal priority.
What is:
2^3×(9−5)+6
A. 30
B. 32
C. 38
D. 44
Double Jeopardy 3
What is:
6+24÷(3×2)
A. 4
B. 8
C. 10
D. 18
Correct Answer: C — 38
Solution
Exponent:
2^3=8
Parentheses:
9−5=4
Multiplication:
8×4=32
Addition:
32+6=38
Strategy
Work through each level of PEMDAS rather than trying to solve the entire expression mentally.
Double Jeopardy 3
Correct Answer: C — 10
Solution
Parentheses:
3×2=6
Division:
24÷6=4
Addition:
6+4=10
Which expression has a value of 72?
A. 2^3×3^2
B. 2^2×3^3
C. 2^4×3^2
D. 2^3×3^3
Correct Answer: A
Solution
Evaluate A:
23=8
32=9
8×9=72
Therefore:
72=23×32
Strategy
When comparing expressions, evaluate the exponents first and then multiply.