Bluebook SAT Test SAT Exponents and Radicals Practice 4 — Questions and Answers
Question 1: Which expression is equivalent to (x^4)^(1/2) × x^(−2)?
- x⁴
- 1 (Correct answer)
- x²
- x^(−4)
Correct answer: 1
(x⁴)^(1/2) = x² and x^(−2) = 1/x². Product = x² · x^(−2) = x⁰ = 1.
Question 2: The half-life of a radioactive element is 10 years. Starting with 640 grams, how many grams remain after 40 years?
- 20
- 40 (Correct answer)
- 80
- 160
Correct answer: 40
40 years = 4 half-lives. Remaining = 640 × (1/2)⁴ = 640/16 = 40 grams.
Question 3: Which of the following equals 2^50 × 4^25?
- 2^75
- 8^75
- 2^100 (Correct answer)
- 16^25
Correct answer: 2^100
4^25 = (2²)^25 = 2^50. So 2^50 × 2^50 = 2^100.
Question 4: Solve: √(3x + 1) = 4
- x = 3
- x = 5 (Correct answer)
- x = 7
- x = 9
Correct answer: x = 5
Square both sides: 3x + 1 = 16 → x = 5.
Question 5: What is the product (2√6)(3√10)?
- 6√60
- 12√15 (Correct answer)
- 6√16
- 12√5
Correct answer: 12√15
(2)(3)√(6×10) = 6√60 = 6·2√15 = 12√15.
Question 6: If x^(1/4) = 3, what is x?
- 9
- 27
- 81 (Correct answer)
- 243
Correct answer: 81
x^(1/4) = 3 → x = 3⁴ = 81.
Question 7: Simplify: (x³y⁻²)^(−2)
- x⁶/y⁴
- y⁴/x⁶ (Correct answer)
- x⁻⁶y⁴
- x⁶y⁴
Correct answer: y⁴/x⁶
x^(3×−2) × y^(−2×−2) = x^(−6) × y⁴ = y⁴/x⁶.
Bluebook SAT Test SAT Exponents and Radicals Practice 4
Which expression is equivalent to (x^4)^(1/2) × x^(−2)?