ASVAB Mathematics Knowledge: Exponents, Radicals, and Ratios — Questions and Answers
Question 1: Simplify: 2³ × 2⁴
- 2⁷ (Correct answer)
- 4⁷
- 2¹²
- 8⁴
Correct answer: 2⁷
When multiplying two powers with the same base, add the exponents: 2³ × 2⁴ = 2^(3+4) = 2⁷. The base stays the same; only the exponents are added.
Question 2: What is √225?
- 13
- 14
- 15 (Correct answer)
- 16
Correct answer: 15
15 × 15 = 225, so √225 = 15. You can verify: 15² = (10+5)² = 100 + 100 + 25 = 225.
Question 3: A recipe requires flour and sugar in a ratio of 3:1. If you use 12 cups of flour, how many cups of sugar are needed?
- 2
- 3
- 4 (Correct answer)
- 6
Correct answer: 4
The ratio 3:1 means for every 3 units of flour there is 1 unit of sugar. With 12 cups of flour: 12 ÷ 3 = 4. So 4 cups of sugar are needed.
Question 4: Which of the following is equivalent to 3.6 × 10³?
- 36
- 360
- 3,600 (Correct answer)
- 36,000
Correct answer: 3,600
Scientific notation: 10³ = 1,000. So 3.6 × 1,000 = 3,600. Moving the decimal point 3 places to the right gives 3,600.
Question 5: What is the value of 5⁰?
- 0
- 1 (Correct answer)
- 5
- Undefined
Correct answer: 1
Any nonzero number raised to the power of 0 equals 1. This follows from the rule: aⁿ ÷ aⁿ = a⁰ = 1. So 5⁰ = 1.
Question 6: If x/4 = 9/12, what is the value of x?
- 2
- 3 (Correct answer)
- 4
- 6
Correct answer: 3
Cross-multiply: 12x = 4 × 9 = 36. Divide both sides by 12: x = 36 ÷ 12 = 3. Alternatively, simplify 9/12 = 3/4, so x = 3.
ASVAB Mathematics Knowledge: Exponents, Radicals, and Ratios
Simplify: 2³ × 2⁴