Exponents and Powers

JCERT · Class 7 · Chapter 5 · Exponents and Powers. Topic notes aligned to the official chapter; these are not solutions to every textbook exercise.

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Why This Chapter Matters

JCERT · Class 7 · Chapter 5 · Exponents and Powers. Topic notes aligned to the official chapter; these are not solutions to every textbook exercise.

Before You Begin (Prerequisites)

Revise relevant arithmetic and ideas from the previous grade.

What You Will Learn (Core Objectives)

Exponents abbreviate repeated multiplication. Add exponents when multiplying equal bases; subtract them when dividing equal nonzero bases. In scientific notation the leading positive number is at least 1 and less than 10.

Chapter Roadmap & Progression

1 Syllabus, textbook and notes alignm...

2 Concept and method

3 Check and common pitfall

Complete Concept Guide (100% Curriculum Coverage)

Syllabus, textbook and notes alignment

JCERT · Regular schools (Non-SOE) · Class 7 · Chapter 5 — Exponents and Powers
Official syllabus pages 89–102. Official syllabus · Prescribed Hindi book (22 chapters) · Separate supplementary reference.

These topic notes and teaching examples are not a complete answer key to every textbook question. English notes use this same JCERT chapter order; a matching English textbook PDF has not been verified.

Official Hindi PDF for this exact chapter

Concept and method

Exponents abbreviate repeated multiplication. Add exponents when multiplying equal bases; subtract them when dividing equal nonzero bases. In scientific notation the leading positive number is at least 1 and less than 10.

Check and common pitfall

Apply equal-base laws only when the bases match.

Key Formulas, Identities & Theorems

Key relationships

$$a^m × a^n = a^(m+n); a^m ÷ a^n = a^(m−n), a ≠ 0; (a^m)^n = a^(mn)$$

Observe the stated conditions and units.

Conceptual Solved Examples & Case Studies

Example 1

Evaluate 2^3 × 2^4 and express 45000 in scientific notation.

Step-by-Step Solution:

2^7 = 128; 45000 = 4.5 × 10^4

Apply equal-base laws only when the bases match.

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