3 to the power of -4 = 0.012345679012
Quick Answer
3 to the power of -4 = 0.012345679012
= 1 / 34 = 0.012345679012 (negative exponent → reciprocal)
Exponents Calculator
Step-by-Step: 3 to the power of -4
A negative exponent means the reciprocal of the base raised to the positive exponent. The general rule is b−n = 1 / bn.
- Rewrite with positive exponent:
3-4 = 1 / 34 - Expand the denominator:
1 / (3 × 3 × 3 × 3) - Compute:
1 / 34 = 0.012345679012
3 to the power of -4 = 0.012345679012
Table of Powers of 3
| n | 3n |
|---|---|
| -5 | 0.004115226337 |
| -4 | 0.012345679012 |
| -3 | 0.037037037037 |
| -2 | 0.111111111111 |
| -1 | 0.333333333333 |
| 0 | 1 |
| 1 | 3 |
| 2 | 9 |
| 3 | 27 |
| 4 | 81 |
| 5 | 243 |
| 6 | 729 |
| 7 | 2187 |
| 8 | 6561 |
| 9 | 19683 |
| 10 | 59049 |
Notation and Properties of Exponents
The expression bn is read as "b to the power of n", where b is the base and n is the exponent. Several common-language equivalents:
- b2 = "b squared" (the area of a square with side b)
- b3 = "b cubed" (the volume of a cube with edge b)
- bn = "b to the nth" (general usage)
Key rules
- Zero Rule: b0 = 1 for any b ≠ 0
- One Rule: 1n = 1 for any n
- Negative exponent: b−n = 1 / bn
- Fractional exponent: b1/n = n√b (e.g. b0.5 = √b)
- Product rule: bm × bn = bm+n
- Power rule: (bm)n = bm·n
Constants supported
This calculator accepts the mathematical constants pi (π ≈ 3.14159) and e (Euler's number ≈ 2.71828), with optional leading minus (-pi, -e) for negative variants.
References
Sample Exponent Calculations
Calculate powers of these numbers:
Related Calculators
- Squared (n²) — exponent fixed at 2
- Cubed (n³) — exponent fixed at 3
- Square Root (√n) — exponent fixed at 1/2
- Cube Root (∛n) — exponent fixed at 1/3
- Logarithm Calculator — the inverse of exponentiation