Exponent Calculator

Calculate powers with any base and exponent, including negative and fractional values.

Result

23 = 8

Understanding Exponents:

  • Positive integer exponents: multiply the base by itself n times
  • Negative exponents: 1 divided by the positive exponent result (e.g., 2-3 = 1/23)
  • Fractional exponents: represents roots (e.g., 20.5 = √2)
  • Zero exponent: any number to the power of 0 equals 1

Three worked examples, one for each exponent type

Positive integer exponent (the default, 2³): multiply the base by itself 3 times.

2³ = 2 × 2 × 2 = 8

Negative exponent (2⁻³): the calculator computes the positive-exponent result first, then takes the reciprocal.

2⁻³ = 1 / 2³ = 1 / 8 = 0.125

Fractional exponent (4^0.5): a 0.5 exponent is equivalent to a square root.

4^0.5 = √4 = 2

Try 8^(1/3) and the tool recognizes it as a cube root, displaying ∛8 = 2 in the explanation rather than just the raw decimal.

Why the zero exponent always returns 1

Any nonzero base raised to the power of 0 equals 1, including negative or fractional bases (e.g., (-5)⁰ = 1, 0.3⁰ = 1). This is a definitional convention that keeps the exponent rules consistent — it isn't something you can verify by "multiplying zero times," since there's no multiplication happening at all.

How large or small results are displayed

Once a result's absolute value exceeds 1,000,000 or falls below 0.000001, the calculator switches to scientific notation (e.g., 10^10 displays as 1.000000e+10) rather than printing a string of digits. Results in between are rounded to 6 decimal places.

Operations this tool won't resolve

Even roots of negative numbers, like (-4)^0.5, produce NaN because JavaScript's Math.pow doesn't return complex numbers — the calculator will show an invalid result rather than i2 (the imaginary answer).