Question

Calcule:

4.(5/3)^3 . (5/3)^-5 .(3/5)^-3 . ∛(27/125) . 1/2 =

Obs.: "^" significa "elevado a"
Por favor preciso das contas

Answer 1

Resposta:

O valor da expressão é igual a 2.

Explicação passo-a-passo:

$x=4\;.\;\left(\dfrac{5}{3}\right)^3\;.\;\left(\dfrac{5}{3}\right)^{-5}\;.\;\left(\dfrac{3}{5}\right)^{-3}\;.\;\sqrt[3]{\dfrac{27}{125}}\;.\;\dfrac{1}{2}\\\\\\x=4\;.\;\dfrac{1}{2}\;.\;\left(\dfrac{5}{3}\right)^3\;.\;\left(\dfrac{5}{3}\right)^{-5}\;.\;\left(\dfrac{5}{3}\right)^3\;.\;\sqrt[3]{\dfrac{3^3}{5^3}}\\\\\\x=\dfrac{4}{2}\;.\;\left(\dfrac{5}{3}\right)^3\;.\;\left(\dfrac{5}{3}\right)^{-5}\;.\;\left(\dfrac{5}{3}\right)^3\;.\;\dfrac{3}{5}$

$x=2\;.\;\left(\dfrac{5}{3}\right)^3\;.\;\left(\dfrac{5}{3}\right)^{-5}\;.\;\left(\dfrac{5}{3}\right)^3\;.\;\left(\dfrac{5}{3}\right)^{-1}\\\\\\x=2\;.\;\left(\dfrac{5}{3}\right)^{(3-5+3-1)}\\\\\\x=2\;.\;\left(\dfrac{5}{3}\right)^{(6-6)}\\\\\\x=2\;.\;\left(\dfrac{5}{3}\right)^0\\\\\\x=2\;.\;1\\\\\\\boxed{x=2}$