Question

Решить : (0,027*а^2*с)^1/3*(1/25*а*с^2/3)^-1/2 зарание

Answer 1

$\left(0.027\cdot a^2\cdot c\right)^{\frac13}\cdot\left(\frac{1}{25}\cdot a\cdot c^{\frac23}\right)^{-\frac12}=\\ =\left(\frac{27}{1000}\cdot a^2\cdot c\right)^{\frac13}\cdot\left(\frac1{25}\cdot a\cdot c^{\frac23}\right)^{-\frac12}=\\ =\left(\left(\frac{3}{10}\right)^3\cdot a^2\cdot c\right)^{\frac13}\cdot\left(\left(\frac15\right)^2\cdot a\cdot c^{\frac23} \right)^{-\frac12}=\\$
$=\left(3^3\right)^\frac13\cdot\left(10^{-3}\right)^{\frac13}\cdot \left(a^2\right)^{\frac13}\cdot c^{\frac13}\cdot\left(5^{-2}\right)^{-\frac12}\cdot a^{-\frac12}\cdot\left(c^{\frac23}\right)^{-\frac12}=\\ =3^{\frac33}\cdot10^{-\frac33}\cdot a^{\frac23}\cdot c^{\frac13}\cdot5^{\frac22}\cdot a^{-\frac12}\cdot c^{-\frac13}=\\ =\frac{3\cdot5}{10}\cdot a^{\frac23-\frac12}\cdot c^{\frac13-\frac13}=\\ =\frac32\cdot a^{\frac{4-3}{3\cdot2}}\cdot c^0=\frac32\cdot a^{\frac16}$