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Mathematics Knowledge: Exponents, Radicals, and Ratios Flashcards

6 cards from real ASVAB practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 Mathematics Knowledge: Exponents, Radicals, and Ratios flashcards as text

  1. Simplify: 2³ × 2⁴

    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.

  2. What is √225?

    Answer: 15

    15 × 15 = 225, so √225 = 15. You can verify: 15² = (10+5)² = 100 + 100 + 25 = 225.

  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?

    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.

  4. Which of the following is equivalent to 3.6 × 10³?

    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.

  5. What is the value of 5⁰?

    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.

  6. If x/4 = 9/12, what is the value of x?

    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.