Question

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

Answer 1

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

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

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

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

$\Rightarrow 2x-2=3$

$\Rightarrow 2x=5$

$\Rightarrow x=\frac{5}{2}$