Chapter 4: Exponents and Powers
3 lessons
An exponent counts how many times a base is multiplied by itself — 2⁴ means 2×2×2×2, or 16. Exponents and Powers covers the laws for combining and simplifying powers without expanding them, negative and zero exponents, and standard form for writing very large or very small numbers.
Reused constantly from here on
These laws don't stay contained to this one chapter — they're used again in Square Roots and Cube Roots later this same year, throughout Class 9 and 10 algebra, and in the scientific notation that shows up in physics and chemistry, where a number like 300,000,000 becomes the far more manageable 3×10⁸.
The two traps
Applying the product law aᵐ×aⁿ=aᵐ⁺ⁿ to terms with different bases is a frequent error — 2³×3² cannot be combined into a single power, since the bases don't match. Confusing a negative exponent with a negative number is the other: a⁻ⁿ means 1/aⁿ, not −aⁿ, so 2⁻³ is 1/8, not −8.