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Value of a negative power

Aviation Mechanic General (AMG) practice question 9 of 25 on Mathematics. ACS element AM.I.H.K10 · difficulty: standard. Want to answer it in a timed quiz? Use the Aviation Mechanic General (AMG) practice mode.

Question bank updated 2026-09-22

QUESTIONWhat is the value of 2⁻³ (2 to the negative 3rd power)?

  1. A−8
  2. B−1/8
  3. C1/8
Show the answer and explanation

Correct answer: C. 1/8

  • A — incorrect A negative exponent does not make the result negative; it makes it a reciprocal.
  • B — incorrect The reciprocal 1/8 is positive; the minus sign in the exponent does not carry into the answer.
  • C — correct A negative power equals the reciprocal with the power made positive: 2⁻³ = 1/2³ = 1/(2 × 2 × 2) = 1/8.

BACKGROUND

A number with a negative power equals its reciprocal with the same power made positive. The handbook example is 2⁻³, read as 2 to the negative 3rd power, calculated as 1/2³ = 1/(2 × 2 × 2) = 1/8. This is the same idea used in powers of ten, where 10⁻² = 1/(10 × 10) = 0.01. When using a calculator to raise a negative number to a power, place parentheses around the negative number so the entire number is raised to the power.

STUDY TIP

Treat a negative exponent as an instruction to flip the number into a fraction, then apply the positive exponent.

KEY POINTS

  • Negative power = reciprocal with a positive power.
  • 2⁻³ = 1/2³ = 1/8.
  • Parenthesize negative bases on a calculator.

SOURCES

  • FAA-H-8083-30B ch03 "Negative Powers"
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SkyDrill is not affiliated with the FAA. This is an original practice item based on FAA-H-8083-30B Aviation Maintenance Technician Handbook – General, 14 CFR part 43 and part 65. Regulations and handbooks are revised; confirm details against the current edition.