Exponent Calculator

Work out bⁿ for any base and exponent, or take the nth root of a number.

Power: bⁿ

2 raised to the power 101,024

Working

  1. 2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024

nth root: ⁿ√x

4th root of 813
Check
3^4 = 81

Exponent rules

RuleExample
bm × bn = bm+n2³ × 2⁴ = 2⁷ = 128
bm ÷ bn = bm−n5⁶ ÷ 5⁴ = 5² = 25
(bm)n = bmn(3²)³ = 3⁶ = 729
b0 = 1 (b ≠ 0)7⁰ = 1
b−n = 1 ÷ bn2⁻³ = 1/8 = 0.125
b1/n = ⁿ√b271/3 = 3

Worked example

2¹⁰

  1. Multiply 2 by itself 10 times
  2. 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024

2¹⁰ = 1,024

Fourth root of 81

  1. Find the number that, multiplied by itself 4 times, gives 81
  2. 3 × 3 × 3 × 3 = 81

⁴√81 = 3

Negative bases

A negative base with a whole-number exponent is fine: (−2)³ = −8 and (−2)⁴ = 16. With a fractional exponent the result is only real when the root is odd — (−8)1/3 = −2, but (−8)1/2 is not a real number. The calculator explains when a result would be complex.