Given:
[tex]5^{8.13}[/tex]
Required:
We need to find the equlivale expression for the given expression.
Explanation:
Consider the decimal value 8.13.
[tex]8.13=8+0.1+0.03[/tex]
Recall that the first digit after the decimal represents the tenths place. The next digit after the decimal represents the hundredths place.
[tex]0.1=\frac{1}{10}[/tex][tex]0.03=\frac{3}{100}[/tex][tex]8.13=8+\frac{1}{10}+\frac{3}{100}[/tex]
The given can be written as follows.
[tex]5^{8.13}=5^{8+\frac{1}{10}+\frac{3}{100}}[/tex][tex]\text{ Use }a^{n+m}=a^n\cdot a^m.[/tex][tex]5^{8.13}=5^8\cdot5^{\frac{1}{10}}\cdot5^{\frac{3}{100}}[/tex]
Final answer:
[tex]5^8\cdot5^{\frac{1}{10}}\cdot5^{\frac{3}{100}}[/tex]
