Ch 12 extends exponents to include negative exponents and explores their applications in expressing very small numbers. Students learn to use standard form (scientific notation) for both large and small numbers.
a⁻ⁿ = 1/aⁿ (a ≠ 0). For example, 2⁻³ = 1/2³ = 1/8. All laws of exponents extend to negative exponents: aᵐ × aⁿ = aᵐ⁺ⁿ works even when m or n is negative.
Same base: aᵐ ÷ aⁿ = aᵐ⁻ⁿ. Reciprocal: (a/b)⁻ⁿ = (b/a)ⁿ. These allow expressing very small numbers: 0.001 = 10⁻³.
Any number can be written as a × 10ⁿ where 1 ≤ a < 10. Large: 384,000,000 = 3.84 × 10⁸. Small: 0.00045 = 4.5 × 10⁻⁴. This is essential in science and engineering.
Download: https://ncert.nic.in/textbook/pdf/hemh112.pdf | Complete book: https://ncert.nic.in/textbook/pdf/hemh1ps.zip
Using the law aᵐ ÷ aᵐ = aᵐ⁻ᵐ = a⁰. Since any number divided by itself is 1, a⁰ = 1 (for a ≠ 0).
Book a Trial + Diagnostic session. Get a personalized Learning Path with clear milestones, tutor match, and a plan recommendation — all within 24 hours.
Book Trial + Diagnostic →