https://file.aiquickdraw.com/mathbot/file/17258976053819a377ji5.jpg

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.

Learn how to simplify the expression 8^(-1) divided by 8^2 using exponent rules. This example demonstrates the application of the division of powers rule and negative exponents. Suitable for students in Grades 7-9.

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