MultiConvers

Exponent Calculator

Raise a base to a power — including negative exponents as reciprocals — and stop at overflow or a non-real negative-base case instead of printing Infinity.

How to use

  1. Enter the base (the number being multiplied).
  2. Enter the exponent (how many times, or the signed power).
  3. Read the power. 2^8 is 256; 2^−3 is 0.125.
  4. Use the root calculator when you mean ⁿ√x rather than typing 1/n as the exponent.

How it works

A positive integer exponent is repeated multiplication: 2^8 = 256. 10^3 = 1,000. 5^0 is 1 for any non-zero 5 — a number to the power 0 is 1. 0^0 is left undefined here; some languages return 1 as a convenience.

A negative exponent is a reciprocal: 2^−3 = 1/8 = 0.125. Fractional exponents are roots when they are real: 9^(1/2) = 3, 8^(1/3) = 2. Negative bases with a fractional exponent such as (−8)^(1/3) may be rejected even though the cube root exists — use the root page for odd roots of negatives.

Overflow past the floating-point range is withheld. 10^400 is not printed as Infinity.

This is not scientific notation (3.2 × 10^4 as a display form) and not a logarithm. To undo a power, use the matching root or the log calculator (log_b of the result is the exponent when the base matches).

A unary minus on a power is not the same as a negative base: −2^4 is −16 if the minus sits outside, and (−2)^4 is +16. Compound-interest (1+r)^n is this page only after you have already formed the base 1+r. Mixed lines such as 2×3^2 belong on the scientific calculator.

Formula

base^exponent
2^8 = 256
2^−3 = 1/8 = 0.125

Worked examples

  • A power of two

    2^8 → 256

  • A negative exponent

    2^−3 → 0.125

Powers of two used as checks

PowerValue
2^01
2^416
2^8256
2^101024
2^−10.5
2^−30.125

Useful notes

  • 0^0 is undefined on this page.
  • Negative base + non-integer exponent is often rejected as non-real.
  • Overflow returns no result, not Infinity.

FAQ

How do I calculate a number raised to a power?

Multiply the base by itself as many times as the exponent. 2^8 is 2×2×2×2×2×2×2×2 = 256.

What does a negative exponent mean?

It is one over the positive power. 2^−3 = 1 / 2^3 = 1/8.

Is 0^0 equal to 1?

This tool treats 0^0 as undefined. Some programming languages return 1; that is a convention, not a settled mathematical value.

What is 5^0?

1. Any non-zero base to the power 0 is 1.

How do I compute 1/16 as a power of 2?

2^−4 = 1/16 = 0.0625.

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