Math Exponents, Radicals, and Scientific Notation — Questions and Answers
Question 1: Simplify: (3²)³
- 729 (Correct answer)
- 18
- 243
- 36
Correct answer: 729
(3²)³ = 3^(2×3) = 3⁶ = 729. When raising a power to a power, multiply the exponents.
Question 2: Which of the following equals 4.5 × 10⁻³?
- 0.0045 (Correct answer)
- 0.045
- 4500
- 45000
Correct answer: 0.0045
A negative exponent moves the decimal left. 4.5 × 10⁻³ = 4.5 ÷ 1000 = 0.0045.
Question 3: Simplify: √72
- 6√2 (Correct answer)
- 8√2
- 36√2
- 4√3
Correct answer: 6√2
72 = 36 × 2 → √72 = √36 × √2 = 6√2.
Question 4: What is the value of 27^(2/3)?
- 9 (Correct answer)
- 3
- 18
- 6
Correct answer: 9
27^(2/3) = (27^(1/3))² = 3² = 9. The denominator of the fractional exponent is the root, and the numerator is the power.
Question 5: Which expression is equivalent to x⁻⁴?
- 1/x⁴ (Correct answer)
- -x⁴
- x⁴
- −1/x⁴
Correct answer: 1/x⁴
A negative exponent means the reciprocal: x⁻ⁿ = 1/xⁿ. So x⁻⁴ = 1/x⁴.
Question 6: The distance from Earth to the Sun is approximately 1.5 × 10⁸ km. The distance from Earth to the Moon is approximately 3.8 × 10⁵ km. Approximately how many times farther is the Sun than the Moon?
- 395 times (Correct answer)
- 3950 times
- 39.5 times
- 3.95 times
Correct answer: 395 times
(1.5 × 10⁸) ÷ (3.8 × 10⁵) = (1.5/3.8) × 10³ ≈ 0.395 × 10³ = 395.
Math Exponents, Radicals, and Scientific Notation
Simplify: (3²)³