Exponents rules incclude product rules, quotient rules, power rules, negative exponents rules, zero rules, one rules, and minus one rules.
| Rule name | Rule | Example |
|---|---|---|
| Product rules | a n · a m = a n+m | 23 · 24 = 23+4 = 128 |
| a n · b n = (a · b) n | 32 · 42 = (3·4)2 = 144 | |
| Quotient rules | a n / a m = a n-m | 25 / 23 = 25-3 = 4 |
| a n / b n = (a / b) n | 43 / 23 = (4/2)3 = 8 | |
| Power rules | (bn)m = bn·m | (23)2 = 23·2 = 64 |
| bnm = b(nm) | 232 = 2(32)= 512 | |
| m√(bn) = b n/m | 2√(26) = 26/2 = 8 | |
| b1/n = n√b | 81/3 = 3√8 = 2 | |
| Negative exponents | b-n = 1 / bn | 2-3 = 1/23 = 0.125 |
| Zero rules | b0 = 1 | 50 = 1 |
| 0n = 0 , for n>0 | 05 = 0 | |
| One rules | b1 = b | 51 = 5 |
| 1n = 1 | 15 = 1 | |
| Minus one rule |
(-1)n = 1 when n is even (-1)n = -1 when n is odd |
(-1)5 = -1 |