Formulas & tables/Mathematics/Powers and roots/Power of a power
Power of a power

Power of a power

(am)n=amn(a^m)^n=a^{mn}

Result unit: — (liczba)

What it describes

When raising a power to another power, multiply the exponents.

Symbols

aa
base
m,nm, n
exponents

Where it comes from

A power of a power means multiplying the same exponent repeatedly, which is why the exponents are multiplied.

When to use it

Simplifying nested powers.

Example

Evaluate (23)2(2^3)^2.
Substitution3⋅2=63\cdot2=6.
Result26=642^6=64.

Related formulas

Product of powers with the same base Root as a fractional power

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