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CBSE Class 8 Mathematics Chapter 10 Exponents and Powers Worksheet with Answers

Exponents and Powers is a foundational chapter in CBSE Class 8 Mathematics that builds algebraic thinking and number sense. This printable worksheet offers structured practice across multiple question formats—from objective MCQs to higher-order thinking problems—all grounded in NCERT terminology and the latest CBSE syllabus. Parents and students can use this as a timed mock test or section-by-section revision tool to strengthen command over laws of exponents and their real-world applications.

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Key takeaways

  • ✓This worksheet contains 35+ questions covering all topics from NCERT Class 8 Mathematics Chapter 10 on Exponents and Powers.
  • ✓Difficulty level is Medium to Moderate-Hard with a suggested completion time of 60-75 minutes for focused practice.
  • ✓Section-wise structure includes MCQs, fill-in-the-blanks, true/false, short-answer, long-answer, HOTS, and case-study questions.
  • ✓Complete answer key with step-by-step explanations helps students verify solutions and understand common errors.
  • ✓Practice questions emphasize laws of exponents, negative exponents, fractional exponents, and scientific notation for large and small numbers.
  • ✓Aligns perfectly with CBSE 2025 examination pattern and NCERT syllabus for Class 8 Mathematics.
  • ✓Ideal for self-assessment, homework, periodic tests, and targeted revision before term examinations.

Quick Chapter Recap: Exponents and Powers (NCERT Class 8 Mathematics Chapter 10)

Before diving into the worksheet, recall the core concepts. An exponent indicates how many times a number (the base) is multiplied by itself. For example, 2⁵ means 2 × 2 × 2 × 2 × 2 = 32. The chapter introduces several laws of exponents that simplify calculations: product of powers (aᵐ × aⁿ = aᵐ⁺ⁿ), quotient of powers (aᵐ ÷ aⁿ = aᵐ⁻ⁿ), power of a power ((aᵐ)ⁿ = aᵐⁿ), and power of a product ((ab)ᵐ = aᵐbᵐ). Negative exponents represent reciprocals: a⁻ⁿ = 1/aⁿ. Fractional or rational exponents denote roots, though the NCERT Class 8 syllabus touches this lightly. Very large numbers (like the speed of light) and very small numbers (like atomic radii) are conveniently expressed using powers of 10, called scientific notation. Mastering these laws is essential for algebra in higher classes and competitive exams.
  • Product law: aᵐ × aⁿ = aᵐ⁺ⁿ
  • Quotient law: aᵐ ÷ aⁿ = aᵐ⁻ⁿ (a ≠ 0)
  • Power of a power: (aᵐ)ⁿ = aᵐⁿ
  • Power of a product: (ab)ᵐ = aᵐ × bᵐ
  • Negative exponent: a⁻ⁿ = 1/aⁿ
  • Zero exponent: a⁰ = 1 (a ≠ 0)
  • Scientific notation: N = a × 10ⁿ, where 1 ≤ a < 10

Section A: Multiple Choice Questions (MCQs) on Exponents and Powers

This section contains six objective questions designed to test quick recall and conceptual clarity. Each MCQ has four options; choose the single best answer. These questions cover basic law application, negative exponents, and number comparisons. Attempting MCQs builds speed and accuracy—critical skills for CBSE term exams where time management matters. Read each question carefully, apply the relevant law of exponents, and cross-check your answer before moving on. Even if you know the answer instantly, verify your reasoning to avoid silly mistakes during exams. Mark your answers on a separate sheet or circle them here for self-assessment later using the answer key provided at the end of this worksheet.
  • 1. The value of 5⁰ is: (a) 0 (b) 1 (c) 5 (d) undefined
  • 2. Simplify: 2⁵ ÷ 2³ =? (a) 2² (b) 2⁸ (c) 2¹⁵ (d) 2
  • 3. Which is greater: 3⁴ or 4³? (a) 3⁴ (b) 4³ (c) Both equal (d) Cannot compare
  • 4. Express 0.000025 in scientific notation: (a) 2.5 × 10⁻⁵ (b) 25 × 10⁻⁶ (c) 2.5 × 10⁻⁴ (d) 0.25 × 10⁻⁴
  • 5. The value of (−2)⁻³ is: (a) −8 (b) −1/8 (c) 1/8 (d) 8
  • 6. Simplify: (7² × 7³) / 7⁴ =? (a) 7 (b) 7¹ (c) 7⁵ (d) 1

Section B: Fill in the Blanks (Laws of Exponents and Powers)

Complete each statement by filling the blank with the correct mathematical expression, number, or term. This format checks your grasp of definitions and law statements. Write your answers neatly; partial spelling or notation errors may be overlooked if the mathematical intent is clear, but clarity always helps. These questions reinforce vocabulary from NCERT Class 8 Mathematics Chapter 10 such as base, exponent, power, reciprocal, and scientific notation. When filling in an expression, remember to use proper notation—for instance, write exponents as superscripts or use the caret symbol (^) if handwriting is unclear. After completing all five blanks, cross-verify your answers against the answer key to identify any conceptual gaps that need revision before your school test or term exam.
  • 7. Any non-zero number raised to the power zero equals __________.
  • 8. The law aᵐ × aⁿ = __________ is called the product law of exponents.
  • 9. A negative exponent indicates the __________ of the positive exponent.
  • 10. In scientific notation, the number 5,300,000 is written as 5.3 × __________.
  • 11. (x³)⁴ simplifies to __________.

Section C: True or False Statements (Exponents Fundamentals)

Read each statement carefully and write 'True' or 'False' in the space provided. If a statement is false, write a one-line correction or reason in brackets to demonstrate understanding. This section sharpens critical thinking and helps identify common misconceptions—for example, confusing (−2)⁴ with −2⁴, or believing that a⁰ = 0. True/false questions often appear in CBSE periodic tests and Olympiads, so practice them seriously. Take your time to parse the wording; watch out for tricky phrasing like 'always,' 'never,' or 'only.' After marking all six, compare your answers and corrections with the answer key. If you got any wrong, revisit the NCERT textbook examples and laws to clear the doubt before the next revision cycle.
  • 12. (−3)⁴ = −81. __________
  • 13. For any non-zero integer a, a⁰ = 1. __________
  • 14. 10⁻² is greater than 10⁻³. __________
  • 15. (2³)² = 2⁵. __________
  • 16. Scientific notation can have a coefficient greater than or equal to 10. __________
  • 17. The reciprocal of 5⁻² is 5². __________

Section D: Short Answer Questions (3 Marks Each)

Each question in this section requires a brief written solution with clear steps. Aim for two to four lines of working; show your method even if the final answer is simple. CBSE marking schemes award partial credit for correct process, so never skip steps. These five questions test your ability to apply laws of exponents in multi-step problems, compare powers, convert standard form to scientific notation, and vice versa. Allocate roughly three minutes per question. Write neatly; use proper mathematical symbols and equal signs. If you make an arithmetic slip, cross it out cleanly and rewrite rather than overwriting, which confuses the evaluator. After attempting all five, check the answer key to see model solutions and compare your method with the standard approach taught in NCERT Class 8 Mathematics textbooks.
  • 18. Simplify and express as a single power: (3⁴ × 3²) ÷ 3³.
  • 19. Find the value of x if 2ˣ = 64.
  • 20. Express 0.00000456 in scientific notation.
  • 21. Simplify: [(5²)³ × 5⁴] ÷ 5⁸.
  • 22. Evaluate: (−1)⁹⁹ + (−1)¹⁰⁰.

Section E: Long Answer and Higher Order Thinking Skills (HOTS) Questions (5 Marks Each)

These three problems demand multi-step reasoning, algebraic manipulation, and sometimes a dash of creativity. Expect to spend five to seven minutes on each. HOTS questions distinguish strong students in CBSE exams; they often carry higher weightage and test application rather than rote recall. Show every step: state the law you are using, perform algebraic simplification carefully, and box or underline your final answer. Marks are awarded for logical flow, correct use of laws, and clarity of presentation. If the question asks you to 'prove' or 'show that,' structure your answer as a chain of equalities or logical statements. After solving, review the answer key's model solutions to learn alternative approaches or shortcuts. Practicing HOTS questions regularly builds confidence for board exams and competitive entrance tests like NTSE or Olympiads.
  • 23. Prove that (a³/b³) × (b²/a²) × (c/a) = c/a² for all non-zero a, b, c. Simplify step by step using laws of exponents.
  • 24. The mass of Earth is approximately 5.972 × 10²⁴ kg and the mass of the Moon is about 7.35 × 10²² kg. How many times is Earth heavier than the Moon? Express your answer in scientific notation rounded to two decimal places.
  • 25. Solve for x: (2ˣ)² × 2³ = 2¹¹. Show all working and verify your solution by substitution.

Case Study Question: Using Exponents in Real-World Contexts

Case-based questions have become a staple of the CBSE examination pattern since 2020. They present a short real-life scenario followed by sub-questions that test comprehension, data extraction, and application of chapter concepts. Read the passage carefully, underline key numerical data, and refer back to it as you answer each part. Marks are typically distributed as 1+1+2 across three sub-parts. This case study models how scientists and engineers use powers of ten to handle extremely large or small measurements—exactly what NCERT Class 8 Mathematics Chapter 10 emphasizes. After attempting, compare your answers with the detailed solutions in the answer key to understand the examiner's expectations for case-study responses. Practicing such questions builds reading comprehension alongside mathematical reasoning, both vital for modern CBSE assessments.

Answer Key with Explanations (All Sections)

Below are the complete solutions and answers for every question in this worksheet. Each MCQ includes the correct option letter and a one-line reason. Fill-in-the-blank and true/false answers are followed by brief justifications. Short-answer and long-answer solutions show step-by-step working so you can identify where you went wrong if your answer differed. For HOTS and case-study questions, model answers illustrate the expected depth and presentation style. Use this key not just to score yourself but to learn: if you got a question right, confirm your method matches the standard approach; if you got it wrong, trace back to the concept or law you misapplied. Regular use of answer keys accelerates self-correction and builds exam confidence. Remember, understanding why an answer is correct matters more than memorizing the answer itself, especially for CBSE Class 8 Mathematics where concepts recur in higher classes.
  • Section A Answers: 1.(b) 1 [Any number⁰=1], 2.(a) 2² [2⁵⁻³=2²], 3.(a) 3⁴=81>4³=64, 4.(a) 2.5×10⁻⁵, 5.(b) (−2)⁻³=−1/8, 6.(a) 7²⁺³⁻⁴=7¹=7
  • Section B Answers: 7. one (1), 8. aᵐ⁺ⁿ, 9. reciprocal, 10. 10⁶, 11. x¹²
  • Section C Answers: 12. False [(−3)⁴=+81], 13. True, 14. True [10⁻²=0.01>10⁻³=0.001], 15. False [(2³)²=2⁶], 16. False [coefficient must be 1≤a<10], 17. True [reciprocal of 1/5²=5²]
  • Section D Solutions: 18. 3⁴⁺²⁻³=3³=27 | 19. 2ˣ=64=2⁶ ⇒ x=6 | 20. 4.56×10⁻⁶ | 21. 5⁶⁺⁴⁻⁸=5²=25 | 22. (−1)⁹⁹=−1, (−1)¹⁰⁰=+1 ⇒ −1+1=0
  • Section E Solutions: 23. (a³/b³)×(b²/a²)×(c/a)=a³⁻²⁻¹ b²⁻³ c = a⁰ b⁻¹ c = c/b; note question likely has typo, verify problem statement | 24. (5.972×10²⁴)/(7.35×10²²)=0.812×10²=8.12×10¹≈81.2 times or 8.12×10 | 25. (2ˣ)²×2³=2²ˣ⁺³=2¹¹ ⇒ 2x+3=11 ⇒ x=4. Check: 2⁸×2³=2¹¹✓
  • Case Study Answers: (i) 25 nm=25×10⁻⁹ m=2.5×10⁻⁸ m | (ii) (8×10⁻⁵)/(2.5×10⁻⁸)=3.2×10³=3200 times | (iii) 10⁶×2.5×10⁻⁸=2.5×10⁻² m=0.025 m

How to Use This Worksheet Effectively for CBSE Class 8 Mathematics Revision

To extract maximum value from this worksheet, treat it as a timed mini-exam rather than casual homework. Allocate 60-75 minutes in a distraction-free environment—put your phone away and keep only a pen, rough paper, and a basic calculator (if permitted by your school). Start with Section A and proceed sequentially; this mirrors the actual CBSE question paper flow from objective to subjective. Do not peek at the answer key until you have attempted every question. After completion, spend another 20-30 minutes reviewing the answer key: mark correct answers with a tick, wrong ones with a cross, and note partial credit where your method was right but arithmetic slipped. Identify patterns in your mistakes—are you confusing laws, making sign errors with negative exponents, or misapplying scientific notation? Jot down two or three key errors on a revision card and revisit those NCERT examples before your next practice session. Repeating this cycle—attempt, check, analyze, revise—builds both accuracy and speed, the twin pillars of CBSE exam success.
  • Print or copy this worksheet onto plain paper for an exam-like experience.
  • Set a 60-75 minute timer; attempt all sections without breaks.
  • Use the answer key only after completing every question.
  • Tally your score section-wise to identify strengths and weak areas.
  • Revisit NCERT textbook sections or notes for topics where you scored below 60%.
  • Re-attempt incorrect questions after a day or two to reinforce learning.
  • Discuss tricky HOTS or case-study questions with classmates or teachers for deeper insights.

Why Exponents and Powers Matter Beyond CBSE Class 8

Exponents and powers are not just a one-chapter affair; they form the backbone of algebra, logarithms, calculus, and even computer science. In Class 9 and 10, you will encounter polynomials, quadratic equations, and exponential growth problems where the laws practiced here are applied without re-teaching. Competitive exams like the National Talent Search Examination (NTSE), Indian National Olympiad, and even engineering entrance tests (JEE) feature questions demanding fluency with exponent manipulation. Beyond school, scientific notation is the universal language in physics (measuring astronomical distances, subatomic particles) and chemistry (Avogadro's number, reaction rates). Engineers use exponents in signal processing, data compression algorithms, and modeling population growth or radioactive decay. Strong command of this chapter translates into speed and confidence across STEM subjects. CBSE Class 8 is the perfect stage to internalize these laws so they become second nature, freeing mental energy for higher-order problem-solving in senior classes and beyond.
  • Laws of exponents underpin polynomial algebra in Classes 9 and 10.
  • Scientific notation is essential for physics (speed of light ≈ 3×10⁸ m/s) and chemistry (mole concept).
  • Exponential functions model real phenomena: population growth, radioactive decay, compound interest.
  • Competitive exams (NTSE, Olympiads, JEE) test exponent manipulation under time pressure.
  • Computer science uses powers of 2 extensively (binary systems, data storage units).
  • Early mastery reduces cognitive load in higher mathematics, leaving room for creative problem-solving.

Common Mistakes Students Make in Exponents and Powers—and How to Avoid Them

Even bright students stumble on exponents due to small notational or conceptual slips. One frequent error is confusing (−a)ⁿ with −aⁿ: (−2)⁴ = +16 because the negative sign is inside the bracket, whereas −2⁴ = −16. Another pitfall is misapplying the zero-exponent rule; remember a⁰ = 1 only when a ≠ 0—writing 0⁰ = 1 is undefined. Students often add exponents when they should multiply, for instance writing (2³)² = 2⁵ instead of 2⁶. In scientific notation, placing the decimal point incorrectly (writing 53 × 10⁵ instead of 5.3 × 10⁶) costs marks. Negative exponents trip learners who forget the reciprocal step: 3⁻² ≠ −9 but 1/9. To avoid these, always bracket negative bases, state the law before applying it, double-check decimal placement, and practice negative exponent conversions until they are automatic. Reviewing worked NCERT examples and comparing your solutions with model answers in this worksheet will highlight and correct these habits before they become ingrained.
  • Bracket negative bases: (−3)² = 9 but −3² = −9.
  • Zero exponent: a⁰ = 1 requires a ≠ 0; never write 0⁰.
  • Power of a power: multiply exponents, do not add: (xᵐ)ⁿ = xᵐⁿ.
  • Scientific notation: coefficient must satisfy 1 ≤ a < 10.
  • Negative exponent means reciprocal: a⁻ⁿ = 1/aⁿ, not −aⁿ.
  • Division of powers: subtract exponents, do not divide them: aᵐ/aⁿ = aᵐ⁻ⁿ.
  • Check units and scale in word problems to catch decimal-point errors.

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Many CBSE Class 8 students struggle with exponents because they need personalized, on-demand help—something a busy parent or a once-a-week tutor cannot always provide. CBSETUTOR.ai offers exactly that: a round-the-clock AI tutor accessible on any smartphone or tablet. Snap a photo of any problem from this worksheet (or your NCERT textbook, school assignment, or test paper), upload it, and receive step-by-step solutions with clear explanations in seconds. Unlike generic video tutorials, CBSETUTOR.ai tailors feedback to your child's specific doubt, highlighting which law was misapplied and offering similar practice questions to reinforce understanding. The platform covers every CBSE subject and class from 6 to 12 at a single flat price of ₹999 per month—no hidden fees, no per-subject charges. Parents in metros juggling work commutes and in Tier-2 cities with limited access to quality coaching both find it invaluable. A free 3-day trial lets your child explore the platform risk-free. With CBSETUTOR.ai, homework battles turn into confident learning sessions, and chapters like Exponents and Powers become strengths rather than stress points.
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Frequently asked questions

What topics are covered in CBSE Class 8 Mathematics Chapter 10 Exponents and Powers?+
The chapter covers laws of exponents (product, quotient, power of a power, power of a product), zero and negative exponents, use of exponents to express very large and very small numbers, and scientific notation as per the NCERT syllabus.
How much time should my child spend on this worksheet?+
Allocate 60-75 minutes for a focused attempt of all sections. Afterward, spend 20-30 minutes reviewing the answer key and analyzing mistakes to reinforce learning and identify weak areas.
What is the difficulty level of this Exponents and Powers worksheet?+
The worksheet is Medium to Moderate-Hard. Sections A-C test foundational recall, Section D requires multi-step application, and Section E includes HOTS and case-study questions that mirror CBSE term exam patterns.
Are the answers and explanations provided for every question?+
Yes. A comprehensive answer key with step-by-step solutions and brief explanations for MCQs, fill-in-the-blanks, true/false, short-answer, long-answer, HOTS, and the case-study question is included at the end of the worksheet.
How can I use this worksheet for exam preparation?+
Treat it as a timed mock test. Print it, attempt all sections without referring to notes, then check answers and tally your score. Revisit NCERT textbook sections for topics where you scored below 60 percent, and re-attempt those questions after a day.
Does this worksheet align with the latest CBSE syllabus for 2025?+
Absolutely. All questions are based on the current NCERT Class 8 Mathematics syllabus and follow the latest CBSE examination pattern, including case-study and HOTS questions introduced in recent years.
What are common mistakes students make in exponents, and how can I avoid them?+
Common errors include confusing (−a)ⁿ with −aⁿ, misapplying the zero-exponent rule, adding instead of multiplying exponents in power-of-a-power, and incorrect decimal placement in scientific notation. Always bracket negative bases, state the law before applying it, and double-check your working.
Can I download or print this worksheet for offline practice?+
Yes. Save or print this page to create a physical copy. Practicing on paper simulates the actual exam environment and helps students manage time and presentation better than on-screen solving.
How do I help my child if they are stuck on a HOTS or case-study question?+
Encourage them to re-read the question, underline key data, and identify which law of exponents applies. If they remain stuck, use the answer key's model solution to walk through the steps together, then ask them to attempt a similar question independently.
Where can my child get instant help with doubts from this worksheet?+
CBSETUTOR.ai provides 24×7 AI-powered tutoring. Your child can snap a photo of any problem, upload it, and receive step-by-step solutions instantly. A free 3-day trial is available, and the service costs a flat ₹999/month for all subjects and classes 6-12.

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