[tex]zad.1\\\\-5\sqrt{7} +2\sqrt{7} =\sqrt{7}(-5+2)= -3\sqrt{7} \\\\zad.2\\\\142^{1} -(10^{3} )^{0} +\sqrt{36} = 142 - 10^{3\cdot 0} +\sqrt{6^{2} } = 142-10^{0} +6^{2\cdot \frac{1}{2} } =142-1+6=147\\\\zad.3\\\\(-2)^{7} \div \sqrt{16} =- 2^{7} \div \sqrt{4^{2} } =- 2^{7} \div 4^{2\cdot \frac{1}{2} } = - 2^{7} \div 4 = - 2^{7} \div 2^{2} = - 2^{7-2} =-2^{5} = - 32\\\\zad.4\\\\\sqrt[3]{(-216)} \cdot (-2\frac{1}{6} )=\sqrt[3]{(-6)^{3} } \cdot (- \frac{13}{6}) = (-6)^{3 \cdot \frac{1}{3} } \cdot (-\frac{13}{6})=[/tex]
[tex]=(-6) \cdot (-\frac{13}{6}) = 13[/tex]
[tex]korzystam~~z~~nastepujacych~~wzorow:\\\\(x^{n} )^{m} = x^{n \cdot m} \\\\\sqrt[n]{x^{n} } =x^{n \cdot \frac{1}{n} } = x\\\\x^{0} =1\\\\(-x)^{n}= - x^{n} ~~gdzie~~n~~jest ~~liczba~~nieparzysta\\\\\\x^{n} \div x^{m} =x^{n-m} \\pamietamy~~rowniez: (-) \cdot(-) = (+)[/tex]