Bluebook SAT Test SAT Exponents and Radicals Practice 3 — Questions and Answers
Question 1: Which of the following is equivalent to x^(−3)?
- −x³
- 1/x³ (Correct answer)
- x^(1/3)
- 3/x
Correct answer: 1/x³
A negative exponent means the reciprocal: x^(−3) = 1/x³.
Question 2: If 3^m = 81 and 3^n = 27, what is m − n?
- 0
- 1 (Correct answer)
- 2
- 3
Correct answer: 1
3^m = 3^4 → m = 4; 3^n = 3^3 → n = 3. m − n = 1.
Question 3: Rationalize the denominator: 6/√3
- 2√3 (Correct answer)
- 3√2
- 6√3
- √18
Correct answer: 2√3
6/√3 × (√3/√3) = 6√3/3 = 2√3.
Question 4: A quantity grows according to y = 500 × 2^(t/5). What is y when t = 15?
- 2,000
- 3,000
- 4,000 (Correct answer)
- 8,000
Correct answer: 4,000
y = 500 × 2^(15/5) = 500 × 2³ = 500 × 8 = 4,000.
Question 5: Simplify: (a²b⁻³)/(a⁻¹b²)
- a³/b⁵ (Correct answer)
- a/b
- a³b⁵
- a⁻³b⁵
Correct answer: a³/b⁵
Subtract exponents: a^(2−(−1)) × b^(−3−2) = a³b^(−5) = a³/b⁵.
Question 6: What is the value of (1/4)^(−3/2)?
- 1/8
- 8 (Correct answer)
- 4√2
- 2
Correct answer: 8
(1/4)^(−3/2) = 4^(3/2) = (√4)³ = 2³ = 8.
Question 7: Simplify: √72 + √50 − √18
- 8√2 (Correct answer)
- 10√2
- 12√2
- 6√2
Correct answer: 8√2
√72 = 6√2, √50 = 5√2, √18 = 3√2. Sum = (6 + 5 − 3)√2 = 8√2.
Bluebook SAT Test SAT Exponents and Radicals Practice 3
Which of the following is equivalent to x^(−3)?