PEAZIT Aha card
Go straight to resources ↓A negative exponent takes the reciprocal
Each decrease of 1 in the exponent divides by the base. After a^0 = 1 comes a^(−1) = 1/a.
| Expression | Meaning |
|---|---|
| 3^1 = 3; 3^0 = 1 | Dividing by three reduces the exponent by 1. |
| 3^(−1) = 1/3 | Divide by three again. |
| 3^(−2) = 1/9 | Once more: 1/(3²). |
One worked example
- 3^1 = 3; 3^0 = 1Dividing by three reduces the exponent by 1.
- 3^(−1) = 1/3Divide by three again.
- 3^(−2) = 1/9Once more: 1/(3²).
Watch out: The base must be nonzero. Brackets distinguish (−2)^(−2) from −2^(−2).
Goal, prerequisites and card origin
What you will learn: Convert a negative integer power to a fraction.
What you need first: Positive powers and reciprocals.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
Each decrease of 1 in the exponent divides by the base. After a^0 = 1 comes a^(−1) = 1/a.