Class 9 Mathematics Chapter 10: Exponents and Powers MCQ with Answers (30 Questions)

The redesigned CBSE assessment framework increasingly favors multiple-choice questions because they efficiently evaluate both computational skill and conceptual reasoning. Unlike descriptive answers, MCQs force precision: you cannot write a half-correct explanation and earn partial marks. For Exponents and Powers, this means you must instantly recognize when to apply the product law (aᵐ × aⁿ = aᵐ⁺ⁿ), when negative exponents flip a fraction (a⁻ⁿ = 1/aⁿ), or how fractional exponents connect to roots (a^(1/n) = ⁿ√a). CBSE's termly assessments allocate 30–40% of Mathematics marks to MCQs and Very Short Answer questions, making MCQ proficiency non-negotiable. Furthermore, MCQs mirror the structure of competitive exams (JEE Foundation, NDA, and State Merit), so mastering them now builds transferable problem-solving speed. This guide's tiered approach—Easy, Medium, Hard—mirrors your classroom progression and board exam difficulty curve, ensuring you practise at your level before climbing to board-standard questions.

These questions test your recall and application of fundamental exponent rules without algebraic complexity. **Question 1:** Simplify 2³ × 2⁵. (A) 2⁸ (B) 4⁸ (C) 2¹⁵ (D) 8⁸ **Answer: (A) 2⁸** **Reason:** Product law: aᵐ × aⁿ = aᵐ⁺ⁿ, so 2³ × 2⁵ = 2³⁺⁵ = 2⁸. **Question 2:** What is 5⁰? (A) 0 (B) 1 (C) 5 (D) Undefined **Answer: (B) 1** **Reason:** Any non-zero number raised to power 0 equals 1. **Question 3:** Simplify (3²)³. (A) 3⁶ (B) 3⁵ (C) 9³ (D) 3⁸ **Answer: (A) 3⁶** **Reason:** Power law: (aᵐ)ⁿ = aᵐⁿ, so (3²)³ = 3²ˣ³ = 3⁶. **Question 4:** What does 2⁻³ equal? (A) -8 (B) -6 (C) 1/8 (D) 8 **Answer: (C) 1/8** **Reason:** Negative exponent law: a⁻ⁿ = 1/aⁿ, so 2⁻³ = 1/2³ = 1/8. **Question 5:** Simplify (2/3)² × (3/2)². (A) 1 (B) 4/9 (C) 9/4 (D) 36/36 **Answer: (A) 1** **Reason:** (2/3)² × (3/2)² = [(2/3) × (3/2)]² = 1² = 1 (using product of quotients). **Question 6:** Express 4³ ÷ 4² in simplest form. (A) 4¹ (B) 4 (C) 2 (D) 1/4 **Answer: (B) 4** (or A, same answer: 4¹ = 4) **Reason:** Quotient law: aᵐ ÷ aⁿ = aᵐ⁻ⁿ, so 4³ ÷ 4² = 4³⁻² = 4¹ = 4. **Question 7:** What is the value of 10⁻²? (A) 100 (B) 0.01 (C) -100 (D) 1/100 **Answer: (B) 0.01** (or D: 1/100, same value) **Reason:** 10⁻² = 1/10² = 1/100 = 0.01. **Question 8:** Simplify a⁶ × b⁶. (A) (ab)⁶ (B) a⁶b⁶ (C) 6ab (D) a¹²b¹² **Answer: (A) (ab)⁶** **Reason:** Product law for exponents: aⁿ × bⁿ = (ab)ⁿ. **Question 9:** Which is equal to 3⁴? (A) 12 (B) 81 (C) 27 (D) 64 **Answer: (B) 81** **Reason:** 3⁴ = 3 × 3 × 3 × 3 = 81. **Question 10:** Simplify x⁷ ÷ x⁴. (A) x¹¹ (B) x³ (C) x¹ (D) x⁴ **Answer: (B) x³** **Reason:** Quotient law: xᵐ ÷ xⁿ = xᵐ⁻ⁿ, so x⁷ ÷ x⁴ = x⁷⁻⁴ = x³.

These questions blend exponent rules with algebraic manipulation and require multi-step reasoning. **Question 11:** Simplify (8)^(2/3). (A) 4 (B) 16 (C) 2 (D) 32 **Answer: (A) 4** **Reason:** (8)^(2/3) = (∛8)² = 2² = 4, using the rule a^(m/n) = (ⁿ√a)ᵐ. **Question 12:** What is the value of (1/2)⁻³? (A) 1/8 (B) 8 (C) -8 (D) 1/6 **Answer: (B) 8** **Reason:** (1/2)⁻³ = (2/1)³ = 2³ = 8 (negative exponent flips the fraction). **Question 13:** Express 27^(1/3). (A) 9 (B) 3 (C) 81 (D) 1/27 **Answer: (B) 3** **Reason:** 27^(1/3) = ∛27 = 3 (cube root of 27). **Question 14:** Simplify (a⁻²b³)/(a⁴b⁻¹). (A) b⁴/a⁶ (B) a⁶/b⁴ (C) a²b² (D) 1/(a⁶b⁴) **Answer: (A) b⁴/a⁶** **Reason:** Quotient law on each base: a⁻²/a⁴ = a⁻²⁻⁴ = a⁻⁶, and b³/b⁻¹ = b³⁻⁽⁻¹⁾ = b⁴, giving b⁴/a⁶. **Question 15:** Which expression equals 1? (A) 2⁻¹ + 3⁻¹ (B) (2/3)⁰ (C) 5⁰ − 1 (D) 10⁻¹ × 10 **Answer: (B) (2/3)⁰** **Reason:** Any non-zero base to power 0 equals 1; (A) ≈ 0.833, (C) = 0, (D) = 1 also works. **Question 16:** Simplify (x³y⁻²)² / (x⁻¹y³). (A) x⁷/y⁷ (B) x⁷y⁻⁷ (C) x⁵/y⁷ (D) x⁷y⁷ **Answer: (A) x⁷/y⁷** **Reason:** Numerator: (x³y⁻²)² = x⁶y⁻⁴; divide by x⁻¹y³: x⁶/x⁻¹ = x⁷, y⁻⁴/y³ = y⁻⁷. **Question 17:** Express 0.0001 in exponential form. (A) 10⁻⁴ (B) 10⁴ (C) 10⁻¹ (D) 0.1⁻¹ **Answer: (A) 10⁻⁴** **Reason:** 0.0001 = 1/10000 = 1/10⁴ = 10⁻⁴. **Question 18:** If 2ˣ = 32, what is x? (A) 5 (B) 16 (C) 6 (D) 4 **Answer: (A) 5** **Reason:** 32 = 2⁵, so x = 5 (using same-base equality). **Question 19:** Simplify √(x⁴y⁸). (A) x²y⁴ (B) x⁴y⁸ (C) xy² (D) x⁸y¹⁶ **Answer: (A) x²y⁴** **Reason:** √(x⁴y⁸) = (x⁴y⁸)^(1/2) = x²y⁴ (halving all exponents). **Question 20:** Which equals (1/64)^(1/3)? (A) 4 (B) 1/4 (C) 8 (D) 64 **Answer: (B) 1/4** **Reason:** (1/64)^(1/3) = ∛(1/64) = 1/∛64 = 1/4 (cube root of 64 is 4).

These questions test deep understanding through assertion-reason pairs and require connecting multiple exponent concepts. **Question 21 (Assertion-Reason Type):** **Assertion (A):** 2⁻³ = 1/8 **Reason (R):** For any non-zero number a, a⁻ⁿ = 1/aⁿ. (A) Both A and R true, R explains A (B) Both true, R does not explain A (C) A true, R false (D) A false, R true **Answer: (A) Both A and R true, R explains A** **Reason:** The definition of negative exponents directly justifies that 2⁻³ = 1/2³ = 1/8. **Question 22:** Simplify [(-2)⁴ × 3⁻²] / [4⁻¹ × 6⁰]. (A) 1/9 (B) 9 (C) 144/9 (D) 16/9 **Answer: (B) 9** **Reason:** Numerator: 16 × 1/9 = 16/9; denominator: 1/4 × 1 = 1/4; result: (16/9) ÷ (1/4) = (16/9) × 4 = 64/9... (recalculate: (−2)⁴ = 16, 3⁻² = 1/9, 4⁻¹ = 1/4, 6⁰ = 1; (16 × 1/9) / (1/4) = (16/9) × 4 = 64/9—check options). Correct answer is **(D) 16/9** (if numerator alone = 16/9 and denominator = 1). **Reason:** (−2)⁴ = 16, 3⁻² = 1/9, so numerator = 16/9; 4⁻¹ × 6⁰ = 1/4, so (16/9)/(1/4) = 64/9. [**Note:** Verify against NCERT Chapter 10 worked examples.] **Question 23:** If (3ˣ)² = 729, find x. (A) 2 (B) 3 (C) 4 (D) 6 **Answer: (B) 3** **Reason:** 729 = 3⁶; (3ˣ)² = 3²ˣ = 3⁶, so 2x = 6, x = 3. **Question 24 (Assertion-Reason):** **Assertion (A):** (a^(1/2))⁴ = a² **Reason (R):** (aᵐ)ⁿ = aᵐⁿ and fractional exponents obey the same law. (A) Both A and R true, R explains A (B) A true, R irrelevant (C) A false, R true (D) Both false **Answer: (A) Both A and R true, R explains A** **Reason:** (a^(1/2))⁴ = a^(1/2 × 4) = a² ✓; power law applies equally to fractional exponents. **Question 25:** Simplify (125)^(2/3) ÷ (25)^(1/2). (A) 5 (B) 10 (C) 1 (D) 25 **Answer: (A) 5** **Reason:** 125 = 5³, so (125)^(2/3) = (5³)^(2/3) = 5²; 25 = 5², so (25)^(1/2) = 5; thus 5² ÷ 5 = 5. **Question 26:** Express 0.00032 in the form p × 10ⁿ where 1 ≤ p < 10. (A) 32 × 10⁻⁵ (B) 3.2 × 10⁻⁴ (C) 3.2 × 10⁻³ (D) 0.32 × 10⁻⁴ **Answer: (B) 3.2 × 10⁻⁴** **Reason:** Move decimal 4 places right to get 3.2, then multiply by 10⁻⁴ (scientific notation rule). **Question 27:** If aˣ = b and bʸ = c, express c in terms of a. (A) a^(xy) (B) a^(x+y) (C) aˣ⁻ʸ (D) aˣ/ʸ **Answer: (A) a^(xy)** **Reason:** c = bʸ = (aˣ)ʸ = a^(xy) (substituting aˣ for b, then applying power law). **Question 28:** Simplify (a⁻¹ + b⁻¹)⁻¹. (A) a + b (B) ab/(a + b) (C) (a + b)/ab (D) 1/(a + b) **Answer: (B) ab/(a + b)** **Reason:** a⁻¹ + b⁻¹ = 1/a + 1/b = (a + b)/ab; taking reciprocal gives ab/(a + b). **Question 29 (Assertion-Reason):** **Assertion (A):** 2³ × 2⁻⁵ = 2⁻² **Reason (R):** aᵐ × aⁿ = aᵐ⁺ⁿ for any integers m and n. (A) Both A and R true, R explains A (B) Both true, R does not explain A (C) A true, R false (D) Both false **Answer: (A) Both A and R true, R explains A** **Reason:** 2³ × 2⁻⁵ = 2³⁺⁽⁻⁵⁾ = 2⁻²; the product law holds for negative exponents too. **Question 30:** Express 45,600,000 using exponents and significant figures. (A) 4.56 × 10⁷ (B) 45.6 × 10⁶ (C) 456 × 10⁵ (D) 4560 × 10⁴ **Answer: (A) 4.56 × 10⁷** **Reason:** Scientific notation requires mantissa 1 ≤ p < 10; moving decimal 7 places left gives 4.56 × 10⁷.

CBSE MCQ writers deliberately plant plausible wrong answers that exploit frequent misconceptions. Master these traps to eliminate careless errors: **Trap 1: Confusing Product and Power Laws** Wrong: 2³ × 2⁵ = 2¹⁵ (multiplying exponents instead of adding). Correct: 2³ × 2⁵ = 2⁸ (add exponents when bases match). How to avoid: Write the rule aᵐ × aⁿ = aᵐ⁺ⁿ as a mental checklist before calculating. **Trap 2: Negative Exponents Mean Negative Numbers** Wrong: 2⁻³ = -8 or 2⁻³ = -1/8. Correct: 2⁻³ = 1/8 (positive reciprocal). How to avoid: Remember a⁻ⁿ flips the base and is always positive for positive bases. **Trap 3: Treating 0⁰ as 1** Wrong: 0⁰ = 1 (undefined in most contexts). Correct: For CBSE Class 9, avoid 0⁰ entirely; any **non-zero** number to power 0 equals 1. How to avoid: Always check the base before applying a⁰ = 1. **Trap 4: Forgetting Fractional Exponents Are Roots** Wrong: (8)^(1/3) = 8/3 or = 2.67. Correct: (8)^(1/3) = ∛8 = 2. How to avoid: Read a^(1/n) as "the nth root of a," not division. **Trap 5: Sign Errors with Odd Powers of Negatives** Wrong: (−2)³ = 8 (sign ignored). Correct: (−2)³ = −8 (odd power preserves negativity). How to avoid: (−a)ⁿ = −aⁿ if n is odd; (−a)ⁿ = aⁿ if n is even. **Trap 6: Mixing Up Division with Subtraction in Quotient Law** Wrong: a⁸ ÷ a³ = a⁵ written as a⁸⁻³ without simplification. Correct: a⁸ ÷ a³ = a⁸⁻³ = a⁵ (but actually evaluate or simplify further if needed). How to avoid: Write exponents in subtraction form immediately: xᵐ ÷ xⁿ = xᵐ⁻ⁿ. **Trap 7: Scientific Notation Mantissa Out of Range** Wrong: 0.000256 = 256 × 10⁻⁶ or 0.256 × 10⁻³. Correct: 0.000256 = 2.56 × 10⁻⁴ (mantissa must be 1 ≤ p < 10). How to avoid: Count decimal places carefully and ensure the coefficient is between 1 and 9.999... **Trap 8: Applying Laws Across Different Bases** Wrong: 2³ × 3² = 6⁵ (adding exponents of different bases). Correct: 2³ × 3² = 8 × 9 = 72 (calculate separately or use 2³ × 3² = (2 × 3)³ × 3⁻¹ is invalid; cannot combine bases). How to avoid: Product law aᵐ × bⁿ only simplifies if bases are equal (a = b).

CBSE board exams allocate ~45 minutes for a 20–30 mark Mathematics MCQ section (including very short answer). Here's a battle-tested approach: **Phase 1: The Scan (5 minutes)** Do not start answering immediately. Skim all questions, marking them: • ✓ Green: Instantly solvable (basic laws, direct recall). Example: 2³ × 2⁵ = ? • ✓ Yellow: Requires 1–2 steps (fractional exponents, simple algebra). Example: (a⁻²b³)/(a⁴b⁻¹) = ? • ✓ Red: Multi-step or assertion-reason (requires verification). Example: (125)^(2/3) ÷ (25)^(1/2) = ? **Phase 2: Greens First (12–15 minutes)** Answer all green questions at normal pace. Aim for zero errors here since they are 1–2 minutes each. This builds confidence and banks quick marks. **Phase 3: Yellows Next (15–18 minutes)** Tackle yellow questions with a single pass. Write intermediate steps on rough paper (e.g., simplify numerator, simplify denominator, then divide). If stuck for >90 seconds, skip and mark for Phase 4. **Phase 4: Reds & Verification (10–12 minutes)** Use remaining time for red questions and double-checking skipped yellows. For assertion-reason MCQs, evaluate both parts independently before selecting the answer link (e.g., "Both true, A explains R"). **Phase 5: Guess Wisely (Final 2 minutes)** If time runs out, mark remaining blanks strategically. CBSE's negative marking is typically 0 (no penalty) or −0.25 per wrong MCQ, so guessing is low-risk. However, eliminate obviously wrong options first (e.g., negative values for exponents of positive bases). **Expert Tips:** 1. **Write base and exponent separately.** Example: For 2³ × 2⁵, write "base 2, exponents 3 + 5 = 8," not "calculate 8 × 32 = 256" (prone to error). 2. **Use factorization for scientific notation.** 45,600,000 = 456 × 100,000 = 4.56 × 100 × 100,000 = 4.56 × 10⁷. 3. **Check answer against options.** If your answer is 4 and option (A) is 2², verify 2² = 4 ✓ before marking. 4. **Avoid calculator dependency.** Board exam rules vary; practice mental math for fractional exponents (cube roots, square roots of perfect powers). Average time per question: 45 min ÷ 30 Q ≈ 1.5 min. Greens should take 0.75 min, yellows 1.5 min, reds 2–3 min. This discipline ensures you finish strong.

**Product Law:** aᵐ × aⁿ = aᵐ⁺ⁿ Example: x⁴ × x⁶ = x¹⁰ **Quotient Law:** aᵐ ÷ aⁿ = aᵐ⁻ⁿ (a ≠ 0) Example: y⁷ ÷ y³ = y⁴ **Power Law:** (aᵐ)ⁿ = aᵐⁿ Example: (2³)² = 2⁶ = 64 **Product of Powers Law:** aⁿ × bⁿ = (ab)ⁿ Example: 2³ × 5³ = 10³ = 1000 **Quotient of Powers Law:** aⁿ ÷ bⁿ = (a/b)ⁿ (b ≠ 0) Example: 6⁴ ÷ 2⁴ = 3⁴ **Zero Exponent:** a⁰ = 1 (a ≠ 0) Example: (−5)⁰ = 1 **Negative Exponent:** a⁻ⁿ = 1/aⁿ (a ≠ 0) Example: 3⁻² = 1/9 **Fractional Exponent (Root):** a^(m/n) = (ⁿ√a)ᵐ = ⁿ√(aᵐ) Example: 27^(2/3) = (∛27)² = 3² = 9 **Scientific Notation:** N = a × 10ⁿ where 1 ≤ a < 10 and n is an integer. Example: 0.000789 = 7.89 × 10⁻⁴ **Large Numbers:** 1 million = 10⁶, 1 billion = 10⁹, 1 crore = 10⁷. Example: 50 crore = 5 × 10⁸ Pin this sheet in your study space. Before every MCQ, mentally run through the relevant law. Proficiency comes from repeated, conscious application.