ASVAB Mathematics Knowledge: Exponents, Radicals, and Ratios

Question 1

Simplify: 2³ × 2⁴

Accepted Answer

2⁷

Answer

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?

Accepted Answer

15

Answer

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?

Accepted Answer

4

Answer

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?

Accepted Answer

3,600

Answer

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?

Accepted Answer

1

Answer

Any nonzero number raised to the power of 0 equals 1. This follows from the rule: aⁿ ÷ aⁿ = a⁰ = 1. So 5⁰ = 1.

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