Schooling · Class 8 · Mathematics · Power Play · Chapter on a page
CBSE Class 8 · Mathematics · NCERT Ganita Prakash Part-I
Power Play: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- Power notation
- Laws of exponents
- Power of a product or quotient
- Zero exponent
- Negative exponents
- Negative bases
- Standard form
- Formulas and facts
- Product of powers
- Quotient of powers
- Power of a power
- Power of a product
- Power of a quotient
- Zero exponent
- Negative exponent
- Worked examples
- Simplify 3⁴ × 3² ÷ 3⁵
- Write 0.000045 in standard form
- Evaluate (−2)⁴ and (−2)⁵
- Watch out for
- Writing 2³ × 2⁴ = 2¹² (multiplying…
- Thinking (−3)² and −3² are the same
- Believing a⁰ = 0
- Forgetting to flip when exponent is…
- Confusing (2³)² with 2³ × 2²
What this chapter is about
This chapter explores the world of exponents and powers, building on what you learnt in Class 7. You will work with powers that have negative bases, compare very large and very small numbers, and learn the laws that make calculations with powers much easier.
Key ideas
- Power notation: In aⁿ, the number a is called the base and n is called the exponent (or index). It means a multiplied by itself n times.
- Laws of exponents: When multiplying powers with the same base, add the exponents (aᵐ × aⁿ = aᵐ⁺ⁿ). When dividing, subtract them (aᵐ ÷ aⁿ = aᵐ⁻ⁿ). When raising a power to another power, multiply the exponents ((aᵐ)ⁿ = aᵐⁿ).
- Power of a product or quotient: (a × b)ⁿ = aⁿ × bⁿ and (a/b)ⁿ = aⁿ/bⁿ.
- Zero exponent: Any non-zero number raised to the power 0 equals 1 (a⁰ = 1, where a ≠ 0).
- Negative exponents: a⁻ⁿ means 1/aⁿ. It flips the base into the denominator.
- Negative bases: When a negative number is raised to an even power, the result is positive; when raised to an odd power, the result is negative.
- Standard form: Very large or small numbers are written as k × 10ⁿ, where 1 ≤ k < 10 and n is an integer.
Formulas and facts to remember
- Rule: Product of powers · Formula: aᵐ × aⁿ = aᵐ⁺ⁿ · Meaning: Same base: add exponents
- Rule: Quotient of powers · Formula: aᵐ ÷ aⁿ = aᵐ⁻ⁿ · Meaning: Same base: subtract exponents
- Rule: Power of a power · Formula: (aᵐ)ⁿ = aᵐⁿ · Meaning: Multiply the exponents
- Rule: Power of a product · Formula: (ab)ⁿ = aⁿbⁿ · Meaning: Distribute the exponent
- Rule: Power of a quotient · Formula: (a/b)ⁿ = aⁿ/bⁿ · Meaning: Distribute the exponent
- Rule: Zero exponent · Formula: a⁰ = 1 (a ≠ 0) · Meaning: Any non-zero base to power 0 is 1
- Rule: Negative exponent · Formula: a⁻ⁿ = 1/aⁿ · Meaning: Flip to denominator, make exponent positive
Common mistakes
- Writing 2³ × 2⁴ = 2¹² (multiplying exponents instead of adding) → When bases are same and you multiply, add the exponents: 2³ × 2⁴ = 2⁷.
- Thinking (−3)² and −3² are the same → (−3)² = 9 but −3² = −9, because without brackets only 3 is squared, then the minus sign is applied.
- Believing a⁰ = 0 → Any non-zero number to the power 0 equals 1, not 0.
- Forgetting to flip when exponent is negative → 5⁻² means 1/5² = 1/25, not −25.
- Confusing (2³)² with 2³ × 2² → (2³)² = 2⁶ (multiply exponents), while 2³ × 2² = 2⁵ (add exponents).
Quick revision
- aᵐ × aⁿ = aᵐ⁺ⁿ (add exponents when multiplying same bases).
- aᵐ ÷ aⁿ = aᵐ⁻ⁿ (subtract exponents when dividing same bases).
- a⁻ⁿ = 1/aⁿ (negative exponent means reciprocal).
- a⁰ = 1 for any a ≠ 0.
- Standard form: k × 10ⁿ where 1 ≤ k < 10.
- Negative base with even power → positive; with odd power → negative.