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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.

Read the first 7 SAT Exponents and Radicals Practice flashcards as text

  1. Which of the following equals (a⁴ × b⁶)^(1/2)?

    Answer: a²b³

    (a⁴b⁶)^(1/2) = a^(4/2) × b^(6/2) = a²b³.

  2. An exponential function is y = 3 × 2^x. What is the percent increase from x = 2 to x = 3?

    Answer: 100%

    At x=2: y=12; at x=3: y=24. Percent increase = (24−12)/12 × 100 = 100%.

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

    Answer: 12

    4^(3/2) = (√4)³ = 8 and 8^(2/3) = (∛8)² = 4. Sum = 8 + 4 = 12.

  4. Simplify: (3^n × 9^n) / 27^n

    Answer: 1

    9^n = 3^(2n) and 27^n = 3^(3n). Numerator = 3^n × 3^(2n) = 3^(3n). Ratio = 3^(3n)/3^(3n) = 1.

  5. Solve: √(2x − 3) = √(x + 7)

    Answer: x = 10

    Square both sides: 2x − 3 = x + 7 → x = 10. Verify: √17 = √17 ✓.

  6. What is the approximate value of 5^(1.5)?

    Answer: 11.18

    5^(1.5) = 5^(3/2) = (√5)³ ≈ (2.236)³ ≈ 11.18.

  7. Which expression is equivalent to (√x + √y)²?

    Answer: x + y + 2√(xy)

    (√x + √y)² = x + 2√(xy) + y = x + y + 2√(xy).