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Exponents, Radicals, and Scientific Notation Flashcards

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

Read the first 6 Exponents, Radicals, and Scientific Notation flashcards as text

  1. Simplify: (3²)³

    Answer: 729

    (3²)³ = 3^(2×3) = 3⁶ = 729. When raising a power to a power, multiply the exponents.

  2. Which of the following equals 4.5 × 10⁻³?

    Answer: 0.0045

    A negative exponent moves the decimal left. 4.5 × 10⁻³ = 4.5 ÷ 1000 = 0.0045.

  3. Simplify: √72

    Answer: 6√2

    72 = 36 × 2 → √72 = √36 × √2 = 6√2.

  4. What is the value of 27^(2/3)?

    Answer: 9

    27^(2/3) = (27^(1/3))² = 3² = 9. The denominator of the fractional exponent is the root, and the numerator is the power.

  5. Which expression is equivalent to x⁻⁴?

    Answer: 1/x⁴

    A negative exponent means the reciprocal: x⁻ⁿ = 1/xⁿ. So x⁻⁴ = 1/x⁴.

  6. The distance from Earth to the Sun is approximately 1.5 × 10⁸ km. The distance from Earth to the Moon is approximately 3.8 × 10⁵ km. Approximately how many times farther is the Sun than the Moon?

    Answer: 395 times

    (1.5 × 10⁸) ÷ (3.8 × 10⁵) = (1.5/3.8) × 10³ ≈ 0.395 × 10³ = 395.

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