Exponents and Scientific Notation
Exponents are a shorthand for repeated multiplication, and they're how scientists write numbers like the distance to the Sun without a page of zeros.
~8 min3 lessonsInteractive converter5-question quiz
01
What a power means
25 = 2 × 2 × 2 × 2 × 2 = 32the small number (exponent) says how many times to multiply the big number (base) by itself
- Anything to the power 1 is itself: 7¹ = 7.
- Anything (except 0) to the power 0 is 1: 7⁰ = 1.
- Negative powers mean “one over”: 2⁻³ = 1/2³ = 1/8.
- Powers of 10 just add zeros: 10⁴ = 10,000.
02
The rules that save time
| Rule | Example |
|---|---|
| Multiply same base: add exponents | 2³ × 2⁴ = 2⁷ |
| Divide same base: subtract exponents | 5⁶ ÷ 5² = 5⁴ |
| Power of a power: multiply exponents | (3²)³ = 3⁶ |
Careful: 2³ × 3⁴ can't be combined that way. The bases are different.
03
Scientific notation
Write a number as a number between 1 and 10 times a power of 10.
| Normal | Scientific notation |
|---|---|
| 150,000,000 km (Earth to Sun) | 1.5 × 10⁸ km |
| 8,200,000,000 (people on Earth, roughly) | 8.2 × 10⁹ |
| 0.000001 m (a micrometre) | 1 × 10⁻⁶ m |
The exponent counts how many places the decimal point moved: left for big numbers (positive), right for small ones (negative). Calculators show it as 1.5E8.
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