Question

Помогите пожалуйста номер 66 и 67

Answer 1

66. 1)
${2}^{ \frac{2}{5} } \times {2}^{ \frac{8}{5} } = {2}^{ \frac{2}{5} + \frac{8}{5} } = {2}^{ \frac{10}{5} } = {2}^{2} = 4$
2)
${5}^{ \frac{3}{8} } \times {5}^{ \frac{5}{8} } = {5}^{ \frac{3}{8} + \frac{5}{8} } = {5}^{ \frac{8}{8} } = {5}^{1} = 5$
3)
${4}^{ \frac{5}{6} } \div {4}^{ \frac{1}{3} } = {4}^{ \frac{5}{6} - \frac{2}{6} } = {4}^{ \frac{3}{6} } = {4}^{ \frac{1}{2} } = 2$
4)
${9}^{ \frac{1}{3} } \div {9}^{ \frac{5}{6} } = {9}^{ \frac{2}{6} - \frac{5}{6} } = {9}^{ - \frac{1}{2} } = \frac{1}{3}$
5) (8^1/15)^-5 = 8^1/15*-5 = 8^-1/3 = 1/2
67. 1) 9^2/5 * 27^2/5 = (3^2)^2/5 * (3^3)^2/5 = (3^2*2/5) * (3^3*2/5) = 3^4/5 * 3^6/5 = 3^4/5+6/5 = 3^10/5 = 3^2 = 9
2) 7^2/3 * 49^2/3 = 7^2/3 * (7^2)^2/3 = 7^2/3 * 7^2*2/3 = 7^2/3 * 7^4/3 = 7^2/3+4/3 = 7^6/3 = 7^2 = 49
3) 144^3/4 ÷ 9^3/4 = (144÷9)^3/4 = 16^3/4 = (2^4)^3/4 = 2^4*3/4 = 2^3 = 8
4) 150^3/2 ÷ 6^3/2 = (150÷6)^3/2 = 25^3/2 = (5^2)^3/2 = 5^2*3/2 = 5^3 = 125