Question

Simplificando a expressão:
(9/10)^7 * (4/3)^9 * (3/5)^6 * (5/6)^11
me ajudem, e expliquem como faz essa questão plissss

Answer 1

Resposta:

A alternativa correta é a letra c.

Explicação passo-a-passo:

$x=\left(\dfrac{9}{10}\right)^7\;.\;\left(\dfrac{4}{3}\right)^9\;.\;\left(\dfrac{3}{5}\right)^6\;.\;\left(\dfrac{5}{6}\right)^{11}\\\\\\x=\left(\dfrac{9}{10}\right)^7\;.\;\left(\dfrac{4}{3}\right)^9\;.\;\left(\dfrac{3}{5}\right)^6\;.\;\left(\dfrac{5}{6}\right)^9\;.\;\left(\dfrac{5}{6}\right)^2\\\\\\x=\left(\dfrac{9}{10}\right)^7\;.\;\left(\dfrac{4}{3}\;.\;\dfrac{5}{6}\right)^9\;.\;\left(\dfrac{3}{5}\right)^6\;.\;\left(\dfrac{5}{6}\right)^2$

$x=\left(\dfrac{9}{10}\right)^7\;.\;\left(\dfrac{20}{18}\right)^9\;.\;\left(\dfrac{3}{5}\right)^6\;.\;\left(\dfrac{5}{6}\right)^2\\\\\\x=\left(\dfrac{9}{10}\right)^7\;.\;\left(\dfrac{10}{9}\right)^9\;.\;\left(\dfrac{3}{5}\right)^6\;.\;\left(\dfrac{5}{6}\right)^2\\\\\\x=\left(\dfrac{9}{10}\right)^7\;.\;\left(\dfrac{10}{9}\right)^7\;.\;\left(\dfrac{10}{9}\right)^2\;.\;\left(\dfrac{3}{5}\right)^6\;.\;\left(\dfrac{5}{6}\right)^2$$x=\left(\dfrac{9}{10}\;.\;\dfrac{10}{9}\right)^7\;.\;\left(\dfrac{10}{9}\;.\;\dfrac{5}{6}\right)^2\;.\;\left(\dfrac{3}{5}\right)^6\\\\\\x=\left(\dfrac{90}{90}\right)^7\;.\;\left(\dfrac{50}{54}\right)^2\;.\;\left(\dfrac{3}{5}\right)^6\\\\\\x=1^7\;.\;\left(\dfrac{25}{27}\right)^2\;.\;\left(\dfrac{3}{5}\right)^6\\\\\\x=\dfrac{25^2}{27^2}\;.\;\dfrac{3^6}{5^6}\\\\\\x=\dfrac{(5^2)^2}{(3^3)^2}\;.\;\dfrac{3^6}{5^6}\\\\\\x=\dfrac{5^4}{3^6}\;.\;\dfrac{3^6}{5^6}$

$x=\dfrac{5^4}{5^6}\\\\\\x=\dfrac{1}{5^2}\\\\\\\boxed{x=\dfrac{1}{25}} \quad \rightarrow \quad \mathbf{letra\;c}$