3 to the power of 4 = 81

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: b^1/n = ⁿ√b (e.g. b^0.5 = √b)
• Product rule: b^m × bⁿ = b^m+n
• Power rule: (b^m)ⁿ = b^m·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.