Question

How would you write it if the exponent is a fraction, for example, 8^-(x/3)=20

Answer 1

Would you multiply by 3 to remove the 3 from the fraction? If so where would you put t in the equation?

Answer 2

you can just separate the fraction and take the power... as such:
\[\huge8^{\frac{-x}{3}}=8^{\frac{1}{3}*-x}=2^{-x}\]
then you just need to log both sides by base 2
\[-x=\log_2(20)\]
kill the negative
\[x=-\log_2(20)\]
or
\[x=-\frac{\ln 20}{\ln 2}\]
if you prefer.