Question

с решением пожалуйста

Answer 1

$\displaystyle\tt 14^{-0.6}\cdot7^{1.6}:2^{-3.6}=2^{-0.6}\cdot7^{-0.6} \cdot7^{1.6}\cdot2^{3.6}=2^{-0.6+3.6}\cdot7^{-0.6+1.6}=\\\\=2^3\cdot7=8\cdot7=56$

$\displaystyle\tt \bigg(\frac{3^{\frac{1}{3}}\cdot3^{\frac{1}{4}}}{\sqrt[12]{\tt3}}\bigg)^2= \bigg(\frac{3^{\frac{1}{3}+\frac{1}{4}}}{3^{\frac{1}{12}}}\bigg)^2= {(3^{\frac{7}{12}-\frac{1}{12}})}^2={(3^{\frac{6}{12}})}^2={(3^{\frac{1}{2}})}^2=3^{\frac{1}{2}\cdot2}=3$

$\displaystyle\tt 0.12^{\frac{1}{9}}\cdot5^{\frac{1}{3}}\cdot15^{\frac{8}{9}}=\bigg(\frac{3}{5^2}\bigg) ^{\frac{1}{9}}\cdot5^{\frac{3}{9}}\cdot5^{\frac{8}{9}}\cdot3^{\frac{8}{9}}=\frac{3^{\frac{1}{9}}}{5^{\frac{2}{9}}}\cdot5^{\frac{11}{9}}\cdot3^{\frac{8}{9}}=3\cdot5=15$