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SAT Exponents and Radicals Practice Flashcards

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

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  1. Which of the following is equivalent to x^(2/3)?

    Answer: ∛(x²)

    The rational exponent 2/3 means the cube root of x squared: x^(2/3) = ∛(x²).

  2. Simplify: (3x²y³)² × (2xy)³

    Answer: 72x⁷y⁹

    (3x²y³)² = 9x⁴y⁶ and (2xy)³ = 8x³y³. Product = 72x^(4+3)y^(6+3) = 72x⁷y⁹.

  3. What is the value of 27^(−2/3)?

    Answer: 1/9

    27^(2/3) = (∛27)² = 3² = 9. The negative exponent gives the reciprocal: 1/9.

  4. If 2^x = 32, what is the value of 2^(x−3)?

    Answer: 4

    2^x = 2^5 so x = 5. Then 2^(5−3) = 2² = 4.

  5. Simplify: √(50x⁴y²)

    Answer: 5x²y√2

    √(50x⁴y²) = √(25·2·x⁴·y²) = 5x²y√2.

  6. Which expression is equivalent to (x^(1/2))(x^(1/3))?

    Answer: x^(5/6)

    Add exponents: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Result is x^(5/6).

  7. What is the value of (8^(1/3) + 16^(1/2)) ÷ 4^(1/2)?

    Answer: 3

    8^(1/3) = 2, 16^(1/2) = 4, 4^(1/2) = 2. (2 + 4)/2 = 3.