Question

Find the value of $x$ for which${\left\{{\left(\frac{-2}{7}\right)}^2\right\}}^x\times {\left(\frac{-7}{2}\right)}^{-1}=\frac{-8}{343}$.

Answer 1

${\left\{{\left(\frac{-2}{7}\right)}^2\right\}}^x+{\left(\frac{-7}{2}\right)}^{-1}=\frac{-8}{343}$

$\Rightarrow {\left(\frac{-2}{7}\right)}^{2x}+\left(\frac{-2}{7}\right)={\left(\frac{-2}{7}\right)}^3$

$\Rightarrow {\left(\frac{-2}{7}\right)}^{2x+1}={\left(\frac{-2}{7}\right)}^3$

$\Rightarrow 2x+1=3$

$\Rightarrow 2x=-2$

$\Rightarrow x=-1$