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 =\[\frac{24}{8}=3\]
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