Algebra Test Exponents and Radicals 1 — Questions and Answers
Question 1: What is the value of 2⁵?
- 10
- 25
- 32 (Correct answer)
- 64
Correct answer: 32
2⁵ means 2 multiplied by itself 5 times: 2×2×2×2×2 = 32.
Question 2: Simplify: x³ · x⁴
- x⁷ (Correct answer)
- x¹²
- 2x⁷
- x
Correct answer: x⁷
When multiplying powers with the same base, add the exponents: x³ · x⁴ = x^(3+4) = x⁷.
Question 3: What is the value of 5⁰?
- 0
- 1 (Correct answer)
- 5
- Undefined
Correct answer: 1
Any nonzero number raised to the power of 0 equals 1.
Question 4: Simplify: (x²)³
- x⁵
- x⁶ (Correct answer)
- x⁸
- 2x⁶
Correct answer: x⁶
When raising a power to a power, multiply the exponents: (x²)³ = x^(2×3) = x⁶.
Question 5: What is √144?
- 11
- 12 (Correct answer)
- 13
- 14
Correct answer: 12
12 × 12 = 144, so √144 = 12.
Question 6: Simplify: x⁶ ÷ x²
- x³
- x⁴ (Correct answer)
- x⁸
- x¹²
Correct answer: x⁴
When dividing powers with the same base, subtract the exponents: x⁶ ÷ x² = x^(6−2) = x⁴.
Question 7: What is the value of 3⁻²?
- -9
- -1/9
- 1/6
- 1/9 (Correct answer)
Correct answer: 1/9
A negative exponent means reciprocal: 3⁻² = 1/3² = 1/9.
