Question

даю 15 балов за решение

Answer 1

$\Large \displaystyle ( \sqrt[4]{32 \cdot \sqrt [3] {4}}+ \sqrt [4] {64 \cdot \sqrt [3] { \frac{1}{2}}}- 3 \sqrt[3]{2 \cdot \sqrt[4]{2}}) \cdot \frac{3}{ \sqrt[12]{2^5}}=$
$\Large \displaystyle ((32 \cdot 4^{ \frac{1}{3}})^{ \frac{1}{4}} + (64 \cdot (\frac{1}{2})^{ \frac{1}{3}})^{ \frac{1}{4}}+3 \cdot (2 \cdot 2^{ \frac{1}{4}})^{ \frac{1}{3}}) \cdot$
$\Large \displaystyle \cdot \frac{3}{2^{\frac{5}{12}}}=((32^{\frac{1}{4}} \cdot 4^{ \frac{1}{12}}})+(64^{ \frac{1}{4}} \cdot (\frac{1}{2})^{\frac{1}{12}}})+3 \cdot 2^{ \frac{1}{3}}\cdot 2^{\frac{1}{12}}) \cdot \frac{3}{2^{\frac{5}{12}}}$
$\Large \displaystyle = ((2^{ \frac{5}{4}} \cdot 2^{ \frac{1}{6}}})+(2^{\frac{3}{2}} \cdot 2^{- \frac{1}{12}}})+3 \cdot 2^{ \frac{1}{3}} \cdot 2^{ \frac{1}{12}}) \cdot \frac{3}{2^{\frac{5}{12}}} =$
$\Large \displaystyle = ((2^{\frac{5}{4}+ \frac{1}{6}})+(2^{\frac{3}{2}- \frac{1}{12}})+3 \cdot 2^{ \frac{1}{3}+ \frac{1}{12}}) \cdot \frac{3}{2^{ \frac{5}{12}}}=$
$\Large \displaystyle = (2^{\frac{17}{12}}+2^{\frac{17}{12}}+3 \cdot 2^{\frac{5}{12}}) \cdot \frac{3}{2^{\frac{5}{12}}}= 2 \cdot \frac{3 \cdot 2^{\frac{17}{12}}}{2^{ \frac{5}{12}}}+ \frac{3 \cdot 3 \cdot 2^{ \frac{5}{12}}}{2^{\frac{5}{12}}}$
$\Large \displaystyle = {2 \cdot 3 \cdot 2^{\frac{12}{12}}}{}+ 3\cdot 3 = 3 \cdot 2 \cdot 2+ 3 \cdot 3 = 12+9 = 21$

Ответ: 21