Question

ПОМОГИТЕ УПРОСТИТЬ ВЫРАЖЕНИЕ ПО ЛОГАРИФМАМ СРОЧНО

Answer 1

$\frac{ \sqrt[4]{36}\cdot \sqrt[3]{500} }{ \sqrt[6]{2}\cdot\sqrt3 }=\frac{ \sqrt[4]{6^2}\cdot 500^{\frac{1}{3}}}{ 2^{\frac{1}{6}}\cdot3^{\frac{1}{2}} }=\frac{ (6^2)^{\frac{1}{4}}\cdot 500^{\frac{1}{3}}}{ 2^{\frac{1}{6}}\cdot3^{\frac{3}{6}} }=$

$\frac{ 6^{\frac{2}{4}}\cdot 500^{\frac{1}{3}}}{2^{\frac{1}{6}}\cdot(3^3)^{\frac{1}{6}} }=\frac{ 6^{\frac{1}{2}}\cdot 500^{\frac{1}{3}}}{(2\cdot3^3)^{\frac{1}{6}}}=\frac{ 6^{\frac{3}{6}}\cdot 500^{\frac{2}{6}}}{(2\cdot3^3)^{\frac{1}{6}}}=$

$\frac{ (6^3)^{\frac{1}{6}}\cdot (500^2)^{\frac{1}{6}}}{(2\cdot3^3)^{\frac{1}{6}} }=\left(\frac{6^3\cdot500^2}{2\cdot3^3} \right)^{\frac{1}{6}}=\left(\frac{(2\cdot3)^3\cdot(2^2\cdot5^3)^2}{2\cdot3^3} \right)^{\frac{1}{6}}=$

$\left(\frac{2^3\cdot3^3\cdot2^4\cdot5^6}{2\cdot3^3} \right)^{\frac{1}{6}}=\left(\frac{2^3\cdot3^3\cdot2^4\cdot5^6}{2\cdot3^3} \right)^{\frac{1}{6}}=\left(\frac{2^7\cdot3^3\cdot5^6}{2\cdot3^3} \right)^{\frac{1}{6}}=$

$\left(2^6\cdot5^6 \right)^{\frac{1}{6}}=2\cdot5=10$