Question

Решите пожалуйста срочно 5 примеров! Заранее спасибо!

Answer 1

$1)5^{\frac{3}{5}}*125*25^{-0,3}*5^{-2,5}=5^{0,6}*5^{3}*(5^{2})^{-0,3}*5^{-2,5}=5^{0,6}*5^{3}*5^{-0,6}*5^{-2,5}=5^{0,6+3-0,6-2,5}=5^{0,5}=5^{\frac{1}{2}}=\sqrt{5}\\\\Otvet:\boxed{\sqrt{5}}$

$2)(\frac{1}{16})^{-0,75}-0,027^{\frac{4}{3}}+(1\frac{61}{64})^{-\frac{2}{3}}=(2^{-4})^{-0,75} -(0,3^{3})^{\frac{4}{3}}+(\frac{125}{64})^{-\frac{2}{3}}=2^{3}-0,3^{4}+((\frac{5}{4})^{3})^{-\frac{2}{3}}=8-0,0081+(\frac{4}{5})^{2}=8-0,0081+0,8^{2}=8-0,0081+0,64=8,6319\\\\Otvet:\boxed{8,6319}$

$3)\frac{(\frac{1}{81})^{-\frac{1}{2}}-(\frac{1}{27})^{-\frac{1}{3}}}{6*125^{\frac{2}{3}}}=\frac{[(9^{-2})]^{-\frac{1}{2}}-[(3^{-3})]^{-\frac{1}{3}}}{6*(5^{3})^{\frac{2}{3}}}=\frac{9-3}{6*5^{2} }=\frac{6}{6*25}=\frac{1}{25}=0,04\\\\Otvet:\boxed{0,04}$

$4)(x^{\frac{3}{4}}*x^{-\frac{1}{3}})^{2\frac{2}{5}}*x^{0,3}*x^{0,7}=(x^{\frac{3}{4}-\frac{1}{3})  }^{\frac{12}{5}}*x^{0,3+0,7}=(x^{\frac{5}{12}})^{\frac{12}{5}}*x=x*x=x^{2}\\\\Otvet:\boxed{x^{2}}$

$5)\frac{\sqrt[4]{x^{3}*\sqrt[3]{x}}}{\sqrt[3]{x^{2}}}=\frac{\sqrt[4]{x^{3} *x^{\frac{1}{3}}}}{x^{\frac{2}{3}}}=\frac{\sqrt[4]{x^{\frac{10}{3}}}}{x^{\frac{2}{3}}}=\frac{x^{\frac{5}{6}}}{x^{\frac{2}{3}}}=x^{\frac{5}{6}-\frac{2}{3}}=5^{\frac{1}{6}}=\sqrt[6]{5}\\\\Otvet:\boxed{\sqrt[6]{5}}$