Bluebook SAT Test SAT Exponents and Radicals Practice 1 — Questions and Answers
Question 1: Which of the following is equivalent to x^(2/3)?
- ∛(x²) (Correct answer)
- x² ÷ x³
- √(x³)
- x^(3/2)
Correct answer: ∛(x²)
The rational exponent 2/3 means the cube root of x squared: x^(2/3) = ∛(x²).
Question 2: Simplify: (3x²y³)² × (2xy)³
- 72x⁷y⁹ (Correct answer)
- 72x⁷y⁸
- 36x⁷y⁹
- 54x⁷y⁹
Correct answer: 72x⁷y⁹
(3x²y³)² = 9x⁴y⁶ and (2xy)³ = 8x³y³. Product = 72x^(4+3)y^(6+3) = 72x⁷y⁹.
Question 3: What is the value of 27^(−2/3)?
- 1/9 (Correct answer)
- 9
- 1/27
- −9
Correct answer: 1/9
27^(2/3) = (∛27)² = 3² = 9. The negative exponent gives the reciprocal: 1/9.
Question 4: If 2^x = 32, what is the value of 2^(x−3)?
- 2
- 4 (Correct answer)
- 8
- 16
Correct answer: 4
2^x = 2^5 so x = 5. Then 2^(5−3) = 2² = 4.
Question 5: Simplify: √(50x⁴y²)
- 5x²y√2 (Correct answer)
- 5xy√2
- 10x²y
- 5x²√(2y)
Correct answer: 5x²y√2
√(50x⁴y²) = √(25·2·x⁴·y²) = 5x²y√2.
Question 6: Which expression is equivalent to (x^(1/2))(x^(1/3))?
- x^(1/6)
- x^(5/6) (Correct answer)
- x^(2/3)
- x^(1/3)
Correct answer: x^(5/6)
Add exponents: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Result is x^(5/6).
Question 7: What is the value of (8^(1/3) + 16^(1/2)) ÷ 4^(1/2)?
- 2.5
- 3 (Correct answer)
- 3.5
- 4
Correct answer: 3
8^(1/3) = 2, 16^(1/2) = 4, 4^(1/2) = 2. (2 + 4)/2 = 3.
Bluebook SAT Test SAT Exponents and Radicals Practice 1
Which of the following is equivalent to x^(2/3)?