Question

Find the value of k forbwhich (-5/11)^7 divided by (-5/11)^k = (-11/5)^2

Answer 1

Dear Student,
Here is the solution of your asked query:
$$\begin{gathered} \frac{{\left({\displaystyle \frac{-5}{11}}\right)}^7}{{\left(\frac{-5}{11}\right)}^{\mathrm{k}}}={\left(\frac{-11}{5}\right)}^2 \\ \Rightarrow {\left(\frac{{\displaystyle -5}}{{\displaystyle 11}}\right)}^{7-\mathrm{k}}={\left(\frac{{\displaystyle -5}}{{\displaystyle 11}}\right)}^{-2}\{\mathrm{since},\frac{{\mathrm{a}}^{\mathrm{m}}}{{\mathrm{a}}^{\mathrm{n}}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}}\mathrm{and}{\left(\frac{\mathrm{a}}{\mathrm{b}}\right)}^{\mathrm{m}}={\left(\frac{{\displaystyle \mathrm{b}}}{{\displaystyle \mathrm{a}}}\right)}^{-\mathrm{m}}\} \\ \Rightarrow 7-\mathrm{k}=-2\{\mathrm{comparing}\mathrm{the}\mathrm{powers}\mathrm{of}\mathrm{both}\mathrm{sides}\} \\ \Rightarrow \mathrm{k}=7+2=9 \end{gathered}$$
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