Formulas & tables/Mathematics/Powers and roots/Root as a fractional power
Root as a fractional power

Root as a fractional power

amn=am/n\sqrt[n]{a^m}=a^{m/n}

Result unit: — (liczba)

What it describes

A root can be written as a power with a fractional exponent.

Symbols

aa
radicand (a≥0a\ge 0)
m,nm, n
natural numbers

Where it comes from

A root is a power with a fractional exponent — the index of the root becomes the denominator of the exponent. This makes computations with powers easier.

When to use it

Converting roots into powers, simplifying expressions.

Example

Write 263\sqrt[3]{2^6} as a power and evaluate it.
Substitution26/32^{6/3}.
Result22=42^2=4.

Related formulas

Power of a power Root of a product

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