Step 1
Given;
Step 2
[tex]\begin{gathered} 5^{8.13}=5^{8+0.13} \\ =5^{8+\frac{1}{10}+\frac{3}{100}} \\ =5^8\times5^{\frac{1}{10}}\times5^{\frac{3}{100}} \end{gathered}[/tex]
Answer; Thus using the law of indices, we have-
[tex]\begin{equation*} 5^8\times5^{\frac{1}{10}}\times5^{\frac{3}{100}} \end{equation*}[/tex]
