Question

solve for x in the given equation:
(5/7)raise to -3*(5/7)raise to -11=(5/7)raise to 7x

Answer 1

$$\begin{gathered} {\left(\frac{5}{7}\right)}^{-3}\times {\left(\frac{5}{7}\right)}^{-11}={\left(\frac{5}{7}\right)}^{7\mathrm{x}} \\ \Rightarrow {\left(\frac{5}{7}\right)}^{-3+\left(-11\right)}={\left(\frac{5}{7}\right)}^{7\mathrm{x}}\left[\mathbf{as}\mathbf{,}\mathbf{}{\mathbf{a}}^{\mathbf{m}}\mathbf{}\mathbf{.}\mathbf{}{\mathbf{a}}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{m}\mathbf{+}\mathbf{n}}\right] \\ \Rightarrow {\left(\frac{5}{7}\right)}^{-14}={\left(\frac{5}{7}\right)}^{7\mathrm{x}} \\ \Rightarrow -14=7\mathrm{x} \\ \Rightarrow \mathrm{x}=-\frac{14}{7}=-2 \end{gathered}$$