Bluebook SAT Test SAT Exponents and Radicals Practice 5 — Questions and Answers
Question 1: What is (5.4 × 10⁶) × (2.0 × 10⁻²) in scientific notation?
- 1.08 × 10⁵ (Correct answer)
- 10.8 × 10³
- 1.08 × 10⁶
- 10.8 × 10⁴
Correct answer: 1.08 × 10⁵
5.4 × 2.0 = 10.8; exponent = 6 + (−2) = 4. So 10.8 × 10⁴ = 1.08 × 10⁵.
Question 2: Which of the following is equivalent to ⁴√(x⁸y⁴)?
- xy
- x²y (Correct answer)
- xy²
- x²y²
Correct answer: x²y
⁴√(x⁸y⁴) = x^(8/4) × y^(4/4) = x²y.
Question 3: If 5^a × 5^b = 5^12 and a − b = 4, what is the value of a?
- 6
- 7
- 8 (Correct answer)
- 10
Correct answer: 8
a + b = 12 and a − b = 4. Adding: 2a = 16, a = 8.
Question 4: Rationalize the denominator of 4/(2 − √3).
- 8 + 4√3 (Correct answer)
- 8 − 4√3
- 4 + 2√3
- 2 + √3
Correct answer: 8 + 4√3
Multiply by (2+√3)/(2+√3): 4(2+√3)/(4−3) = 4(2+√3) = 8 + 4√3.
Question 5: Solve for x: 9^(2x) = 27
- x = 3/4 (Correct answer)
- x = 2/3
- x = 1
- x = 3/2
Correct answer: x = 3/4
9^(2x) = 3^(4x) and 27 = 3³. So 4x = 3, x = 3/4.
Question 6: What is the simplified form of √45 ÷ √5?
- √9
- 3 (Correct answer)
- 9
- 3√5
Correct answer: 3
√45 ÷ √5 = √(45/5) = √9 = 3.
Question 7: An investment grows as A = 1000 × (1.06)^t. Using log 2 ≈ 0.301 and log 1.06 ≈ 0.0253, in how many years does it approximately double?
- 10
- 11
- 12 (Correct answer)
- 14
Correct answer: 12
1.06^t = 2 → t = log2/log1.06 ≈ 0.301/0.0253 ≈ 11.9 ≈ 12 years.
Bluebook SAT Test SAT Exponents and Radicals Practice 5
What is (5.4 × 10⁶) × (2.0 × 10⁻²) in scientific notation?