The expression in the image is:

$\frac{8^{-1}}{8^2}$

Solution:

Using the properties of exponents, we can simplify this expression. The rule for dividing powers with the same base is:

$\frac{a^m}{a^n} = a^{m-n}$

In this case, $a = 8$, $m = -1$, and $n = 2$, so:

$\frac{8^{-1}}{8^2} = 8^{-1-2} = 8^{-3}$

Now, simplify $8^{-3}$:

$8^{-3} = \frac{1}{8^3}$

And calculate $8^3$:

$8^3 = 512$

Thus, the final answer is:

$\frac{1}{512}$

Would you like more details or have any questions?

Related Questions:

1. How do you simplify expressions with negative exponents?
2. What are the general exponent rules for multiplication and division?
3. How can you express powers of 8 in terms of smaller factors?
4. What does a negative exponent indicate in an equation?
5. How does $8^3$ relate to cube roots?

Tip: When dividing terms with the same base, remember that you subtract the exponents.