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Equivalent Expressions 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^(1/2))(x^(3/2))?

    Answer: x²

    x^(1/2) · x^(3/2) = x^(1/2 + 3/2) = x^(4/2) = x².

  2. Which of the following is equivalent to (a²b³)/(ab)?

    Answer: ab²

    a²/a = a and b³/b = b², so the result is a · b² = ab².

  3. Which expression is equivalent to −3(2x − 5) + 4x?

    Answer: −2x + 15

    −6x + 15 + 4x = −2x + 15.

  4. Which expression is equivalent to x² + 6x + 9?

    Answer: (x + 3)²

    x² + 6x + 9 fits the pattern a² + 2ab + b² = (a + b)² with a = x, b = 3.

  5. Which of the following is equivalent to (4x³ + 8x² − 12x)/(4x)?

    Answer: x² + 2x − 3

    Divide each term: 4x³/4x + 8x²/4x − 12x/4x = x² + 2x − 3.

  6. Which of the following is equivalent to (1/x) + (1/x²)?

    Answer: (x + 1)/x²

    Find common denominator x²: x/x² + 1/x² = (x + 1)/x².

  7. Which of the following is equivalent to (5x⁴)²?

    Answer: 25x⁸

    (5x⁴)² = 5² · (x⁴)² = 25 · x⁸ = 25x⁸.