question_answer

Find x, such that \[{{\left( \frac{1}{5} \right)}^{5}}\times {{\left( \frac{1}{5} \right)}^{19}}={{\left( \frac{1}{5} \right)}^{8x}}\]

Answer:

Given, \[{{\left( \frac{1}{5} \right)}^{5}}\times {{\left( \frac{1}{5} \right)}^{19}}={{\left( \frac{1}{5} \right)}^{8x}}\] \[{{\left( \frac{1}{5} \right)}^{5+19}}={{\left( \frac{1}{5} \right)}^{8x}}\]                                                            \[\left[ \therefore {{a}^{m}}\times {{a}^{n}}={{a}^{m+n}} \right]\]             \[{{\left( \frac{1}{5} \right)}^{24}}={{\left( \frac{1}{5} \right)}^{8x}}\] When bases are equal, then by equating their exponents, we get 8x = 24 ∴                      x =\[\frac{24}{8}=3\]