Ch 11 covers exponents (powers) — a shorthand for repeated multiplication. Students learn the laws of exponents, express large numbers in standard form, and compare extremely large and small numbers.
aⁿ means a multiplied by itself n times. Here a is the base and n is the exponent. For example: 2⁵ = 2×2×2×2×2 = 32. Any non-zero number raised to power 0 equals 1.
Same base: aᵐ × aⁿ = aᵐ⁺ⁿ and aᵐ ÷ aⁿ = aᵐ⁻ⁿ. Power of a power: (aᵐ)ⁿ = aᵐⁿ. Same exponent: aᵐ × bᵐ = (ab)ᵐ.
Standard form expresses a number as a × 10ⁿ, where 1 ≤ a < 10. Example: 384,000,000 = 3.84 × 10⁸. This is useful for expressing very large or very small numbers.
Download: https://ncert.nic.in/textbook/pdf/gemh111.pdf | Complete book: https://ncert.nic.in/textbook/pdf/gemh1ps.zip
Using the law aⁿ ÷ aⁿ = aⁿ⁻ⁿ = a⁰. Since any number divided by itself is 1, a⁰ = 1 (for a ≠ 0).
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