[tex](0,25^{-2,5}\cdot16^{\frac{1}{4}})^{\frac{1}{3}}-\sqrt{10}^{2}-8^{2}=[(\frac{25}{100})^{-\frac{25}{10}}\cdot(4^{2})^{\frac{1}{4}}]^{\frac{1}{3}}-10-64=\\\\=[(\frac{1}{4})^{-\frac{5}{2}}\cdot4^{2\cdot\frac{1}{4}}]^{\frac{1}{3}}-74 = (4^{\frac{5}{2}}\cdot4^{\frac{1}{2}})^{\frac{1}{3}}-74 = (4^{\frac{5}{2}+\frac{1}{2}})^{\frac{1}{3}}-74=(4^{3})^{\frac{1}{3}}-74=\\\\=4^{3\cdot\frac{1}{3}} - 74 =4-74 = - 70[/tex]
Wyjaśnienie
Wykorzystano własności potęg:
[tex]a^{-n} = (\frac{1}{a})^{n}\ \ \ dla \ a \neq 0\\\\a^{m}\cdot a^{n} = a^{m+n}\\\\(a^{m})^{n} = a^{m\cdot n}[/tex]
