What it does
An exponent counts how many times you multiply by the base: 2³ = 2 × 2 × 2. This page draws each power as a row of tiles: solid means ”× a”, dashed means ”÷ a”. Then the laws happen in front of you:
- aᵐ × aⁿ = aᵐ⁺ⁿ: the rows join.
- aᵐ ÷ aⁿ = aᵐ⁻ⁿ: solid and dashed pairs cancel.
- (aᵐ)ⁿ = aᵐⁿ: n rows of m tiles.
- aᵐ × bᵐ = (ab)ᵐ: pair each a with a b.
Exact values check that both sides agree. A ladder of a³, a², a¹, a⁰, a⁻¹ shows why a⁰ = 1 and a⁻ⁿ = 1/aⁿ. A Level switch allows negative exponents for Class 9.
It fits Class 8 Mathematics, power play (laws of exponents). Next, see fast growth in doubling power, very large numbers in standard form, or another tile rule in algebraic identity tiles.
How to use it
- Pick a law.
- Drag the sliders for a (and b) and exponents m and n, or type values.
- Read the big line, the tiles, then “Check with values”, which ends in a tick when the law holds.
A worked example
2³ × 2⁴: 3 tiles plus 4 tiles, nothing cancels, so 2⁷. Check: 8 × 16 = 128 = 2⁷.
For 2³ ÷ 2⁴, 3 solid tiles cancel 3 of the 4 dashed ones, leaving 1 dashed: 2⁻¹ = 1/2. Check: 8 ÷ 16 = 1/2.
(2³)⁴ is 4 rows of 3 tiles: 2¹² = 4,096. And 2³ × 5³ = 10³ = 1,000.
Common mistakes
- 2³ × 2⁴ is not 2¹²: rows join, they are not repeated.
- 2³ × 3⁴ cannot become one power: the bases differ.
- 2⁻³ is 1/8, not negative.
Check yourself
Five fresh questions, one for each law and one negative exponent. Press Check; open the worked answer if needed. Nothing is saved.
FAQ
Why is a⁰ = 1? Multiplying by nothing leaves 1. The ladder shows a¹ ÷ a = 1.
Is this from the NCERT book? It covers the same topic with fibub’s own pictures and examples. fibub is not part of NCERT.
Where the numbers come from
- The laws of exponents for integer and rational exponents are standard algebra. Pictures, wording and examples are fibub's own.
- Checked against Python's fractions.Fraction (exact a**m * a**n, a**m / a**n, (a**m)**n and a**m * b**m) for every base 2 to 10 and every exponent from −6 to 8.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-10.