[tex]dla \ \ x = 2^{4}\\\\(x^{\frac{5}{8}}-x^{\frac{3}{8}})^{2} = ((2^{4})^{\frac{5}{8}}-(2^{4})^{\frac{3}{8}})^{2} = (2^{\frac{5}{2}}-2^{\frac{3}{2}})^{2} = (2^{\frac{5}{2}})^{2}-2\cdot2^{\frac{5}{2}}\cdot2^{\frac{3}{2}}+(2^{\frac{3}{2}})^{2}=\\\\=2^{5}-2\cdot2^{4}+2^{3} = 32-2\cdot16+8 = 32-32+8 =\boxed{ 8}[/tex]
Wykorzystano własności potęg:
[tex](a^{n})^{m} = a^{n\cdot m}\\\\a^{n}\cdot a^{m} =a^{n+m}[/tex]
oraz wzór skróconego mnożenia:
[tex](a-b)^{2} = a^{2}-2ab + b^{2}[/tex]
