We'll use the follwowing property, which comes from the definition of a logarithm:
[tex]\log _ab=c\Leftrightarrow a^c=b[/tex]i.e, The logarithm with base a of b is c if, and only if a to the c power equals b.
Using this to translate
[tex]\log _5(\frac{1}{25})=-2[/tex]Into exponential form, will yield:
[tex]5^{-2}[/tex]Because:
[tex]5^{-2}=\frac{1}{25}[/tex]ANSWER:
[tex]5^{-2}[/tex]