Bluebook SAT Test Equivalent Expressions 3 — Questions and Answers
Question 1: Which of the following is equivalent to (x^(1/2))(x^(3/2))?
- x
- x² (Correct answer)
- x³
- x^(3/4)
Correct answer: x²
x^(1/2) · x^(3/2) = x^(1/2 + 3/2) = x^(4/2) = x².
Question 2: Which of the following is equivalent to (a²b³)/(ab)?
- ab
- ab² (Correct answer)
- a²b²
- a³b⁴
Correct answer: ab²
a²/a = a and b³/b = b², so the result is a · b² = ab².
Question 3: Which expression is equivalent to −3(2x − 5) + 4x?
- −2x + 15 (Correct answer)
- −2x − 15
- 10x − 15
- 2x + 15
Correct answer: −2x + 15
−6x + 15 + 4x = −2x + 15.
Question 4: Which expression is equivalent to x² + 6x + 9?
- (x + 3)(x − 3)
- (x + 3)² (Correct answer)
- (x − 3)²
- (x + 9)(x + 1)
Correct answer: (x + 3)²
x² + 6x + 9 fits the pattern a² + 2ab + b² = (a + b)² with a = x, b = 3.
Question 5: Which of the following is equivalent to (4x³ + 8x² − 12x)/(4x)?
- x² + 2x − 3 (Correct answer)
- 4x² + 8x − 12
- x² + 2x + 3
- x³ + 2x² − 3x
Correct answer: x² + 2x − 3
Divide each term: 4x³/4x + 8x²/4x − 12x/4x = x² + 2x − 3.
Question 6: Which of the following is equivalent to (1/x) + (1/x²)?
- 2/x²
- (x + 1)/x² (Correct answer)
- 1/x³
- 2/x
Correct answer: (x + 1)/x²
Find common denominator x²: x/x² + 1/x² = (x + 1)/x².
Question 7: Which of the following is equivalent to (5x⁴)²?
- 10x⁶
- 25x⁶
- 10x⁸
- 25x⁸ (Correct answer)
Correct answer: 25x⁸
(5x⁴)² = 5² · (x⁴)² = 25 · x⁸ = 25x⁸.
Bluebook SAT Test Equivalent Expressions 3
Which of the following is equivalent to (x^(1/2))(x^(3/2))?