Formulas & tables/Mathematics/Powers and roots/Power with a negative exponent
Power with a negative exponent

Power with a negative exponent

a−n=1ana^{-n}=\dfrac{1}{a^n}

Result unit: — (liczba)

What it describes

A power with a negative exponent is the reciprocal of the power with the positive exponent.

Symbols

aa
base (a≠0a\neq 0)
nn
exponent

Where it comes from

A negative exponent means the reciprocal — “move it to the denominator and change the sign of the exponent.”

When to use it

Expressions with negative exponents, scientific notation.

Example

Evaluate 2−32^{-3}.
Substitution123\dfrac{1}{2^3}.
Result18=0.125\dfrac{1}{8}=0.125.

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