Question

calcule $<var>5^{x}^{+3}=\sqrt[3]{1/25}</var>$

Answer 1

$5^{x+3}= \sqrt[3]{\frac{1}{25}}$

Se elevarmos à potência negativa, o numerador inverte com o denominador.

$5^{x+3}= \sqrt[3]{(\frac{25}{1})^{-1}} \\\\ fatorando \ o \ 25 \\\\ 5^{x+3}= \sqrt[3]{(5^{2})^{-1}} \\\\ 5^{x+3}= \sqrt[3]{5^{-2}}} \\\\ tirando \ o \ 5 \ da \ raiz \\\\ 5^{x+3}= 5^{-\frac{2}{3}} \\\\ quando \ as \ bases \ s\~{a}o \ iguais, elas \ se \ anulam$

$x+3=-\frac{2}{3} \\\\ x = -\frac{2}{3}-3 \\\\ MMC=3 \\\\ x = -\frac{2}{3}-\frac{9}{3} \\\\ \boxed{\boxed{x = -\frac{11}{3}}}$