[tex]zad.9\\\\(\sqrt[4]{9} \cdot 27 )^{4} =(\sqrt[4]{3^{2} } \cdot 3^{3} )^{4}=( (3^{2} )^{\frac{1}{4} } \cdot 3^{3} )^{4}= ( 3^{2\cdot \frac{1}{4} } \cdot 3^{3} )^{4}= ( 3^{ \frac{1}{2} } \cdot 3^{3} )^{4}=(3^{\frac{1}{2} +3} )^{4} =(3^{3\frac{1}{2}} )^{4} =(3^{\frac{7}{2}} )^{4} =3^{\frac{7}{2} \cdot 4} =3^{14} \\\\\\(\sqrt[4]{9} \cdot 27 )^{4} =3^{14} \\\\(\sqrt[4]{9} \cdot 27 )^{4} =3^{14} =3^{2\cdot 7 } =(3^{2} )^{7} =9^{7}[/tex]
korzystam ze wzorów:
[tex]\sqrt[n]{x^{m} } =x^{m\cdot \frac{1}{n} } \\\\x^{n} \cdot x^{m} =x^{n+m} \\\\(x^{n} )^{m} =x^{m\cdot n}[/tex]
