Задание 3. Упростите выражение: а) (32243)25+(2)0⋅(81)−12; 6) 5√27⋅128⋅5√9.

Задание 3.

а) ((\(\frac{32}{243}\))^{\frac{2}{5}}\) + (\(\frac{2}{5}\))^0 ⋅ (\(\frac{81}{16}\))^{-\frac{1}{2}}\) = ((\(\frac{2^5}{3^5}\))^{\frac{2}{5}}\) + 1 ⋅ (\(\frac{3^4}{2^4}\))^{-\frac{1}{2}}\) = ((\(\frac{2}{3}\))^5)^{\frac{2}{5}}\) + (\(\frac{3}{2}\))^{-2}\) = (\(\frac{2}{3}\))^2 + (\(\frac{2}{3}\))^2 = \(\frac{4}{9}\) + \(\frac{4}{9}\) = \(\frac{8}{9}\)

б) ⁵√27 ⋅ 128 ⋅ ⁵√9 = ⁵√3³ ⋅ 2⁷ ⋅ ⁵√3² = ⁵√3⁵ ⋅ 2⁷ = 3 ⋅ ⁵√2⁷ = 3 ⋅ 2 ⋅ ⁵√2² = 6 ⋅ ⁵√4