Important Questions: CBSE Class 8 Mathematics Chapter 10 Exponents and Powers

Chapter 10 Exponents and Powers introduces students to the systematic rules governing repeated multiplication, extending earlier work from Class 7. The NCERT textbook covers three main areas: the seven fundamental laws of exponents (product, quotient, power-of-power, zero exponent, negative exponent, and fractional bases), negative exponents and their reciprocal interpretation, and the use of powers of 10 to express very large numbers (like distances in astronomy) or very small numbers (like sizes of microorganisms). In the CBSE Class 8 annual examination, this chapter typically accounts for 6-8 marks distributed across 2-3 questions. Expect one 1-mark objective question (MCQ or fill-in-the-blank), one 2-mark or 3-mark simplification problem, and often a 3-5 mark application-based or case-based question linking exponents to science or data interpretation. The chapter pairs naturally with Chapter 11 Direct and Inverse Proportions and Chapter 12 Factorisation for algebraic reasoning. Strong performance here builds the foundation for Class 9 topics like polynomials and rationalisation.

One-mark questions from Exponents and Powers usually appear as MCQs or fill-in-the-blank items in Section A of the CBSE paper. These test instant recall of exponent laws, recognition of equivalent forms, and quick computation. Expect questions on zero exponent (a^0 = 1 for a ≠ 0), negative exponent as reciprocal (a^(−n) = 1/a^n), or identifying the base and exponent in a given power. Speed and accuracy matter; no working is required, but double-check sign and base before marking your answer. Below are five typical 1-mark questions with answers.

Two-mark questions require one or two steps of working and usually involve simplifying an expression using two laws, or evaluating a numerical power. CBSE awards 1 mark for method and 1 mark for the correct final answer. Always write the law you are applying (e.g. 'using a^m × a^n = a^(m+n)') to secure method marks even if arithmetic slips occur. Show intermediate steps clearly. Common question types include combining product and quotient laws, expressing a number in standard form, or solving for an unknown exponent. Below are four typical 2-mark questions with model solutions.

Three-mark questions in CBSE Class 8 Mathematics test deeper understanding and require three to four distinct steps. Typical formats include simplifying complex nested expressions, proving an identity using exponent laws, or solving equations where the unknown appears in the exponent. Marks are split: 1 for writing the relevant law or stating the approach, 1 for intermediate working, and 1 for the final answer. Always box or underline your final answer. If you make an arithmetic error midway, partial marks are still awarded for correct method. Below are four important 3-mark questions modelled on past CBSE papers.

Five-mark questions are the longest in the CBSE Class 8 paper and often combine exponent laws with a real-world scenario or data interpretation. Recent CBSE papers include case studies: a passage about astronomical distances measured in light-years (powers of 10), bacterial growth rates (exponential doubling), or computer memory sizes (powers of 2). You must read the passage, extract numerical data, apply exponent laws, and answer sub-questions (typically 1+1+3 or 2+3 marks). Marks are awarded for comprehension, correct law application, intermediate calculations, and final answers. Neat presentation and labelled steps are crucial. Below are two representative 5-mark questions.

CBSE question-setters follow predictable patterns when drafting items for Chapter 10. Understanding these patterns helps you anticipate question types and allocate revision time efficiently. First, every paper includes at least one direct-law question: simplify an expression using product, quotient, or power-of-power rules. Second, standard-form (scientific notation) questions appear almost every year, either as stand-alone 2-markers or embedded in case studies. CBSE loves real-world hooks—astronomical distances, microscopic measurements, population figures, data storage—because these test mathematical modelling alongside computation. Third, negative and zero exponents are favourite traps in MCQs; options are designed to catch students who forget the reciprocal rule or misapply the zero-exponent law to the number zero itself. Fourth, since 2020 CBSE has introduced competency-based and case-based items, so expect a 4-5 mark passage with sub-questions requiring interpretation, calculation, and reasoning. Finally, proof or 'show that' questions (3 marks) test conceptual depth: you must justify each step with a named law rather than simply compute. Recognising these five archetypes means you can practise strategically, focusing on past-paper questions that match the pattern rather than working through random exercises.

Even strong students lose marks in Exponents and Powers through careless errors. The most frequent mistake is sign confusion with negative exponents: writing 2^(−3) = −8 instead of 1/8, or treating a^(−n) as negative rather than reciprocal. Always remember the negative exponent rule means 'flip to denominator', not 'make negative'. Second, the power-of-power law trips many: students write (a^m)^n = a^(m+n) instead of a^(mn), mixing it with the product law. Drill the difference: same base multiplied → add exponents; power raised to power → multiply exponents. Third, zero-exponent errors abound. Remember a^0 = 1 only when a ≠ 0; the expression 0^0 is undefined, and CBSE sometimes includes it as a distractor. Fourth, in standard form, students often miscount decimal shifts, writing 0.00045 as 4.5 × 10^(−4) instead of 4.5 × 10^(−4); count carefully and double-check the sign of the exponent. Fifth, students drop or change the base during multi-step simplifications. If you start with powers of 2, every intermediate step must remain powers of 2 until explicitly converted. Sixth, skipping steps in working costs method marks; even if your final answer is correct, show the law name and intermediate result. Finally, time pressure in the exam leads to misreading questions—read twice, underline key data, and ensure your answer matches the question asked (e.g. 'express in standard form' vs 'express as a single power').

Forty-eight hours before your exam, consolidate your understanding with this quick-reference formula sheet and revision checklist. Write the seven laws of exponents on a postcard: (1) a^m × a^n = a^(m+n), (2) a^m ÷ a^n = a^(m−n), (3) (a^m)^n = a^(mn), (4) (ab)^n = a^n b^n, (5) (a/b)^n = a^n / b^n, (6) a^0 = 1 (a≠0), (7) a^(−n) = 1/a^n. Memorise the standard-form template: a number is in standard form if written as k × 10^n where 1 ≤ k < 10 and n is an integer. Practise five representative problems—one from each question type above—under timed conditions. Review your marked practice papers and list every error; if you confused product and power laws twice, do ten focused drills on that law pair. On exam day, read each exponent question twice, underline the base and all exponents, decide which laws apply, then execute step-by-step. Use the margin for rough work but copy cleanly into the answer booklet. For case-based questions, underline numerical data in the passage and match each sub-question to the relevant law before calculating. Finally, double-check units and form: if the question asks for standard form, do not leave your answer as 450 × 10^6—convert it to 4.5 × 10^8. These small checks secure full marks and distinguish top scorers from average performers.

Exponents and Powers can feel abstract at first, especially when juggling negative and fractional indices or multi-step simplifications under exam pressure. CBSETUTOR.ai provides a 24×7 AI tutor that explains every law with interactive examples, checks your working step-by-step, and catches errors before they become habits. Simply snap a photo of any problem—from NCERT Exercise 10.1 or a tricky case-based question—and receive an instant, fully worked solution with law names highlighted at each stage. The platform covers all CBSE classes (6-12) at a single flat rate of ₹999 per month, so your child can revise Exponents in Class 8 and preview Polynomials for Class 9 without paying extra. Unlike coaching centres that run on fixed timetables, CBSETUTOR.ai adapts to your schedule: practice at 6 a.m. before school, clarify doubts at 10 p.m. after dinner, or binge-solve problems on Sunday afternoon. Parents in metro cities like Delhi, Bengaluru and Mumbai appreciate the convenience—no commute, no waitlists—while families in Tier-2 towns gain access to the same quality of instruction as expensive city coaching. Start with the 3-day free trial: upload five exponent problems, explore the question bank, and see how instant feedback accelerates learning. One mother from Pune reported her daughter jumped from 4/8 to 8/8 in Chapter 10 after just two weeks of daily photo-upload practice, because every mistake was explained immediately rather than waiting for the next tutor session.