Bluebook SAT Test SAT Exponents and Radicals Practice 2 — Questions and Answers
Question 1: If a = 3 × 10⁵ and b = 6 × 10³, what is a/b expressed in scientific notation?
- 5 × 10¹ (Correct answer)
- 0.5 × 10³
- 5 × 10⁻¹
- 5 × 10²
Correct answer: 5 × 10¹
a/b = (3/6) × 10^(5−3) = 0.5 × 10² = 5 × 10¹.
Question 2: Simplify: (x³)^(2/3)
- x² (Correct answer)
- x^(9/2)
- x^(1/3)
- x⁶
Correct answer: x²
(x³)^(2/3) = x^(3 × 2/3) = x² by the power-of-a-power rule.
Question 3: Which of the following equals (√3 + √2)(√3 − √2)?
- 1 (Correct answer)
- √6
- 5
- √5
Correct answer: 1
Using difference of squares: (√3)² − (√2)² = 3 − 2 = 1.
Question 4: A bacteria colony triples every 4 hours. Starting with 200 bacteria, which expression gives the count after t hours?
- 200 × 3^t
- 200 × 3^(t/4) (Correct answer)
- 200 × (1/3)^(t/4)
- 200 × 4^(t/3)
Correct answer: 200 × 3^(t/4)
The count triples every 4 hours, so the formula is 200 × 3^(t/4).
Question 5: What is the simplified form of ∛(27x⁶y³)?
- 3x²y (Correct answer)
- 3x²y²
- 9x²y
- 3xy³
Correct answer: 3x²y
∛(27x⁶y³) = ∛27 × ∛(x⁶) × ∛(y³) = 3 × x² × y = 3x²y.
Question 6: Solve for x: 4^x = 8
- x = 1
- x = 3/2 (Correct answer)
- x = 2
- x = 3
Correct answer: x = 3/2
4^x = 2^(2x) and 8 = 2³. So 2x = 3, x = 3/2.
Question 7: Simplify: (16)^(3/4)
- 4
- 8 (Correct answer)
- 12
- 24
Correct answer: 8
16^(3/4) = (⁴√16)³ = 2³ = 8.
Bluebook SAT Test SAT Exponents and Radicals Practice 2
If a = 3 × 10⁵ and b = 6 × 10³, what is a/b expressed in scientific notation?