Question

qual o valor para x na equação?

Answer 1

$3^ \frac{2}{5}^x=3^-^4 \\ \\ x=-10$

Answer 2

Propriedades utilizadas:

$a^{x}=a^{y}~~~\therefore~~~\boxed{\boxed{x=y}}~~~~~(sendo~a\ \textgreater \ 0~e~\neq1)\\\\\sqrt[y]{a^{x}}\rightleftharpoons a^{(x/y)}\\\\\dfrac{1}{a^{x}}\rightleftharpoons a^{-x}\\\\(a^{x})^{y}\rightleftharpoons a^{xy}$
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$(\sqrt[5]{3^{2}})^{x}=\frac{1}{81}\\\\\\(3^{(2/5)})^{x}=\frac{1}{3^{4}}\\\\\\3^{(2/5)\cdot x}=3^{-4}$

Bases iguais (e positivas e diferentes de 1), iguale os expoentes:

$\dfrac{2}{5}\cdot x=-4~~~\therefore~~~x=(-4)\cdot\dfrac{5}{2}=(-2)\cdot5~~~\therefore~~~\boxed{\boxed{x=-10}}$