Question

Вычеслить: в числителе 15^ 2 /3 *3 ^ 7/3 в знаменателе: 5-^1/3

Answer 1

15^(2/3) * 3^(7/3) / 5^(-1/3) = 3^(2/3) * 5^(2/3) * 3^(7/3) * 5^(1/3) = 

3^((2+7)/3) * 5^((2+1)//3) = 3^3 * 5^1 = 27 * 5 = 135

Answer 2

$\\\frac{15^{\frac{2}{3}}\cdot 3^{\frac{7}{3}}}{5^{-\frac{1}{3}}}=\\ \frac{5^{\frac{2}{3}}\cdot 3^{\frac{2}{3}}\cdot 3^{\frac{7}{3}}}{5^{-\frac{1}{3}}}=\\ 5^{\frac{2}{3}-(-\frac{1}{3})} \cdot 3^{\frac{9}{3}}=\\ 5^{\frac{3}{3}}\cdot 3^3=\\ 5\cdot 27=\\ 135$