Question

Преобразуйте данное выражение к виду n√А 1)√2*³√32)⁴√2*⁶√33)⁴√3b³ *√3b

Answer 1

$1) sqrt{2}sqrt[3]{3} = 2^frac{1}{2}cdot3^frac{1}{3} = 2^frac{1*3}{2*3}cdot 3^frac{1*2}{3*2} = 2^frac{3}{6}cdot3^frac{2}{6} = (2^3)^frac{1}{6}cdot(3^2)^frac{1}{6} =\\= (2^3cdot3^2)^frac{1}{6} = (8cdot9)^frac{1}{6} = boxed{sqrt[6]{72}}$

$2) sqrt[4]{2}sqrt[6]{3} = 2^frac{1}{4}cdot3^frac{1}{6} = 2^frac{1*3}{4*3}cdot3^frac{1*2}{6*2} = 2^frac{3}{12}cdot3^frac{2}{12} = (2^3)^frac{1}{12}cdot(3^2)^frac{1}{12} =\\= (2^3cdot3^2)^frac{1}{12} =(8cdot9)^frac{1}{12} = boxed{sqrt[12]{72}}$

$3) sqrt[4]{3b^3}sqrt{3b} = (3b^3)^frac{1}{4}cdot(3b)^frac{1}{2} = (3b^3)^frac{1}{4} cdot(3b)^frac{2}{4} = (3b^3)^frac{1}{4}cdot(9b^2)^frac{1}{4} =\\= (27b^5)^frac{1}{4} = boxed{sqrt[4]{27b^5}}$