The expression in the image is:

$\left( \frac{3}{8} \right)^5 \times \left( \frac{3}{8} \right)^4 \div \left( \frac{3}{8} \right)^9$

To simplify this, we can apply the laws of exponents. Specifically, when multiplying powers with the same base, you add the exponents. When dividing powers with the same base, you subtract the exponents.

Step-by-Step Solution:

1. Multiply the first two terms: $\left( \frac{3}{8} \right)^5 \times \left( \frac{3}{8} \right)^4 = \left( \frac{3}{8} \right)^{5+4} = \left( \frac{3}{8} \right)^9$

2. Divide by the third term: $\frac{\left( \frac{3}{8} \right)^9}{\left( \frac{3}{8} \right)^9} = \left( \frac{3}{8} \right)^{9-9} = \left( \frac{3}{8} \right)^0$

3. Simplify: Any non-zero number raised to the power of zero is 1, so: $\left( \frac{3}{8} \right)^0 = 1$

Thus, the simplified result is:

$\boxed{1}$

Let me know if you'd like further details or have questions!

Related Questions:

1. What are the general laws of exponents used in this problem?
2. How do you handle negative exponents in similar problems?
3. Can this method be used with variables instead of constants?
4. How would this change if one of the fractions was raised to a negative power?
5. What happens if the base is a complex fraction?

Tip:

Always check if you can apply the laws of exponents (multiplication, division, or power rules) when simplifying expressions.