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Exponents and Radicals Flashcards

7 cards from real Algebra 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 Exponents and Radicals flashcards as text

  1. What is the product √3 · √12?

    Answer: 6

    √3 · √12 = √(3 × 12) = √36 = 6.

  2. Simplify: (x³ · x⁻¹) / x²

    Answer: 1

    x³ · x⁻¹ = x², then x² / x² = x⁰ = 1.

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

    Answer: x√x

    x^(3/2) = x^1 · x^(1/2) = x · √x = x√x.

  4. Rationalize the denominator of 1/√5.

    Answer: √5/5

    Multiply by √5/√5: (1 · √5)/(√5 · √5) = √5/5.

  5. What is the value of (-8)^(1/3)?

    Answer: -2

    (-8)^(1/3) is the cube root of -8; since (-2)³ = -8, the answer is -2.

  6. Simplify: √(4x²y⁴), assuming x ≥ 0 and y ≥ 0

    Answer: 2xy²

    √4 = 2, √x² = x, and √y⁴ = y², so √(4x²y⁴) = 2xy².

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

    Answer: 4

    8^(2/3) = (8^(1/3))² = 2² = 4.