( a m ) n = a m ⋅ n {\displaystyle (a^{m})^{n}=a^{m\cdot n}}
Dlaczego to działa? Sprawdźmy na przykładzie.
Zapisz ( 2 3 ) 2 {\displaystyle \left(2^{3}\right)^{2}} w postaci 2 n {\displaystyle 2^{n}} .
Możemy to rozpisać jako ( 2 ⋅ 2 ⋅ 2 ) 2 = ( 2 ⋅ 2 ⋅ 2 ) ⋅ ( 2 ⋅ 2 ⋅ 2 ) = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 2 6 {\displaystyle (2\cdot 2\cdot 2)^{2}=(2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2=2^{6}}
To się zgadza z wzorem ( a m ) n = a m ⋅ n {\displaystyle (a^{m})^{n}=a^{m\cdot n}} :
( 2 3 ) 2 = 2 3 ⋅ 2 = 2 6 {\displaystyle \left(2^{3}\right)^{2}=2^{3\cdot 2}=2^{6}}
w postaci 
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