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Quiz: Exponents and Powers

Test your understanding of exponents, powers, and radical expressions with these questions.

1. What is the value of any non-zero number raised to the power of zero?

  1. Zero
  2. One
  3. The number itself
  4. Undefined
Show Answer

The correct answer is B. Any non-zero number raised to the power of zero equals 1. This follows from the pattern of decreasing exponents: when you divide by the base repeatedly (like 2³ = 8, 2² = 4, 2¹ = 2), continuing the pattern gives 2⁰ = 1. This rule holds for any base except zero itself, which is undefined.

Concept Tested: Zero Exponent

See: Zero Exponent

2. Which expression correctly represents the negative exponent rule?

  1. b⁻ⁿ = -bⁿ
  2. b⁻ⁿ = 1/bⁿ
  3. b⁻ⁿ = b/n
  4. b⁻ⁿ = n/b
Show Answer

The correct answer is B. The negative exponent rule states that b⁻ⁿ = 1/bⁿ, meaning a negative exponent represents the reciprocal of the base raised to the positive exponent. Option A incorrectly applies the negative sign to the result. Options C and D confuse exponents with division operations. For example, 2⁻³ = 1/2³ = 1/8.

Concept Tested: Negative Exponents

See: Negative Exponents

3. When multiplying x⁵ · x³, what is the simplified result?

  1. x¹⁵
  2. x⁸
  3. x²
  4. 2x⁸
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The correct answer is B. Using the Product Rule for Exponents, when multiplying powers with the same base, you add the exponents: x⁵ · x³ = x⁵⁺³ = x⁸. Option A incorrectly multiplies the exponents (5 × 3 = 15). Option C incorrectly subtracts the exponents. Option D incorrectly adds a coefficient of 2.

Concept Tested: Product Rule for Exponents

See: Product Rule

4. A scientist measures a bacteria sample at 0.0000047 meters. How would this be written in scientific notation?

  1. 4.7 × 10⁻⁶
  2. 4.7 × 10⁶
  3. 47 × 10⁻⁷
  4. 0.47 × 10⁻⁵
Show Answer

The correct answer is A. To convert 0.0000047 to scientific notation, move the decimal point 6 places to the right to get 4.7, and since we moved right, the exponent is negative: 4.7 × 10⁻⁶. Option B has a positive exponent, which would represent a large number. Options C and D don't follow the scientific notation format where 1 ≤ |a| < 10.

Concept Tested: Scientific Notation

See: Scientific Notation

5. Simplify the expression (x²)⁵.

  1. x⁷
  2. x¹⁰
  3. x³²
  4. 5x²
Show Answer

The correct answer is B. Using the Power Rule for Exponents, when raising a power to another power, multiply the exponents: (x²)⁵ = x²·⁵ = x¹⁰. Option A incorrectly adds the exponents (2 + 5 = 7). Option C incorrectly raises 2 to the power of 5 (2⁵ = 32). Option D treats the outer exponent as a coefficient.

Concept Tested: Power Rule for Exponents

See: Power Rule

6. What does the expression √49 equal?

  1. 24.5
  2. 7
  3. ±7
  4. 49²
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The correct answer is B. The square root symbol √ represents the principal (positive) square root, so √49 = 7 because 7² = 49. While both 7 and -7 when squared equal 49, by convention the square root symbol gives only the positive value. Option A incorrectly divides 49 by 2. Option C includes both roots, which is not the standard meaning of the radical symbol. Option D represents 49 squared, not its square root.

Concept Tested: Square Root

See: Square Root

7. Simplify y⁷/y³.

  1. y⁴
  2. y¹⁰
  3. y²¹
  4. 7/3
Show Answer

The correct answer is A. Using the Quotient Rule for Exponents, when dividing powers with the same base, subtract the exponents: y⁷/y³ = y⁷⁻³ = y⁴. Option B incorrectly adds the exponents (7 + 3 = 10). Option C incorrectly multiplies the exponents (7 × 3 = 21). Option D treats the expression as pure numerical division.

Concept Tested: Quotient Rule for Exponents

See: Quotient Rule

8. Which of the following expressions is NOT a polynomial?

  1. 3x² + 5x - 7
  2. x⁴ - 2x² + 1
  3. 1/x + 2
  4. 7
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The correct answer is C. A polynomial must have only non-negative integer exponents. The expression 1/x can be rewritten as x⁻¹, which has a negative exponent, so it is not a polynomial. Options A and B are polynomials with positive integer exponents. Option D is a constant polynomial (degree 0), which is valid.

Concept Tested: Polynomial

See: What is a Polynomial

9. To simplify √72, you would first factor it as 36 × 2. What is the reasoning behind choosing these factors?

  1. 36 and 2 are both even numbers
  2. 36 is the largest perfect square that divides 72
  3. 36 and 2 add up to 38
  4. 2 is a prime number
Show Answer

The correct answer is B. When simplifying radicals, we look for the largest perfect square factor because we can take its square root and move it outside the radical. Since 36 = 6², we can write √72 = √(36 × 2) = 6√2. While option A is true, being even is not the key criterion. Options C and D mention irrelevant properties that don't help with simplification.

Concept Tested: Simplifying Radicals

See: Simplifying Radicals

10. If you multiply (3 × 10⁴) · (2 × 10⁵), what is the result in scientific notation?

  1. 5 × 10⁹
  2. 6 × 10⁹
  3. 6 × 10²⁰
  4. 5 × 10²⁰
Show Answer

The correct answer is B. When multiplying numbers in scientific notation, multiply the coefficients and add the exponents: (3 × 10⁴) · (2 × 10⁵) = (3 · 2) × 10⁴⁺⁵ = 6 × 10⁹. Option A incorrectly adds the coefficients (3 + 2 = 5). Options C and D incorrectly multiply the exponents instead of adding them (4 × 5 = 20).

Concept Tested: Scientific Notation

See: Operations with Scientific Notation

Quiz Complete

Review the explanations above to reinforce your understanding of exponents and powers. For additional practice, refer back to the chapter content.