Simplify the Fraction Expression: 27 Divided by 3^8

First, let's note that 27 is a power of the number 3:

$27=3^3$Using this fact gives us a situation where in the fraction's numerator and denominator we get terms with identical bases, let's apply this to the problem:

$\frac{27}{3^8}=\frac{3^3}{3^8}$Now let's recall the law of exponents for division between terms without identical bases:

$\frac{a^m}{a^n}=a^{m-n}$ Let's apply this law to the last expression we got:

$\frac{3^3}{3^8}=3^{3-8}=3^{-5}$where in the first stage we applied the above law and in the second stage we simplified the expression we got in the exponent,

Let's summarize the solution steps, we got:

$\frac{27}{3^8}=\frac{3^3}{3^8}=3^{-5}$Therefore the correct answer is answer D.