Odpowiedź:
[tex]\dfrac{2^{2} \cdot (\frac{1}{8} )^{\frac{1}{4} } \cdot \sqrt{32} }{8^{\frac{1}{4} } } =\dfrac{2^{2} \cdot ((\frac{1}{2} )^{3} )^{\frac{1}{4} } \cdot \sqrt{2^{5} } }{(2^{3} )^{\frac{1}{4} } }=\dfrac{2^{2} \cdot (\frac{1}{2} )^{\frac{3}{4} }\cdot (2^{5} )^{\frac{1}{2} } }{2^{\frac{3}{4} } } =\dfrac{2^{2} \cdot 2^{-\frac{3}{4} }\cdot 2^{\frac{5}{2} } }{2^{\frac{3}{4} } } =\dfrac{2^{2-\frac{3}{4} +\frac{5}{2} } }{2^{\frac{3}{4} } } =[/tex]
[tex]\dfrac{2^{2-\frac{3}{4} +\frac{10}{4} } }{2^{\frac{3}{4} } } =\dfrac{2^{2+\frac{7}{4} } }{2^{\frac{3}{4} } } =\dfrac{2^{3\frac{3}{4} } }{2^{\frac{3}{4} } } =2^{3\frac{3}{4} -\frac{3}{4} } =2^{3} =2\cdot 2\cdot 2 =8[/tex]
Korzystam ze wzorów:
[tex]\sqrt[n]{x} =x^{\frac{1}{n} } \\\\x^{n} \cdot x^{m} =x^{n+m} \\\\x^{n} \div x^{m} =x^{n-m} \\\\x^{n} =(\frac{1}{x} )^{-n}[/tex]
