Negative Exponent Calculator

Work out negative exponent instantly with clear inputs, formula shown and shareable results.

About Negative Exponent Calculator

A negative exponent means take the reciprocal: b⁻ⁿ = 1/bⁿ. It follows from the quotient rule, since b⁰⁻ⁿ = b⁰ ÷ bⁿ = 1/bⁿ.

Formula

Negative exponent

b⁻ⁿ = 1 / bⁿ

Worked example

With the default values below, Negative Exponent Calculator returns b⁻ⁿ of 0.0080000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Base b: 5
Positive exponent n (used as −n)minimum 0: 3

Results

b⁻ⁿ: 0.0080000000
bⁿ: 125.000000
As a fraction: 1/125
1/b: 0.20000000

Step by step

1Values used
2Negative exponent
3b⁻ⁿ= 0.0080000000
4bⁿ= 125.000000
5As a fraction= 1/125
61/b= 0.20000000

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is 5⁻³?

1/125 = 0.008.

Does a negative exponent make the answer negative?

No. It makes it a reciprocal. 5⁻³ is a small positive number, not a negative one.