Сначала найдем значение (∛36/∛49)^-3/2:
∛36 = 3, ∛49 = 7
(3/7)^-3/2 = (3/7)^-1.5 = 1/(3/7)^1.5 = 1/(3^1.5/7^1.5) = 1/(√(3^3)/√(7^3)) = 1/(3√3/7√7) = 7√7/3√3 = 7√7/3√3 * √3/√3 = 7√21/9
Теперь у нас получилось (7√21/9)*6^2:
(7√21/9)6^2 = (7√21/9)(6^2) = (7√21/9)*36 = 252√21/9 = 28√21
Итак, (∛36/∛49)^-3/2*6^2 = 28√21.
Сначала найдем значение (∛36/∛49)^-3/2:
∛36 = 3, ∛49 = 7
(3/7)^-3/2 = (3/7)^-1.5 = 1/(3/7)^1.5 = 1/(3^1.5/7^1.5) = 1/(√(3^3)/√(7^3)) = 1/(3√3/7√7) = 7√7/3√3 = 7√7/3√3 * √3/√3 = 7√21/9
Теперь у нас получилось (7√21/9)*6^2:
(7√21/9)6^2 = (7√21/9)(6^2) = (7√21/9)*36 = 252√21/9 = 28√21
Итак, (∛36/∛49)^-3/2*6^2 = 28√21.