I see you've uploaded an image with a mathematical expression. Let me analyze and solve it for you.

The expression is:

$c = \frac{360}{\sqrt{18}} + \frac{5}{(5 - 3\sqrt{2})^{2023}} \cdot \frac{(10 - 6\sqrt{2})^{2024}}{2^{2022}}$

Let me break this down step by step.

1. Simplifying $\frac{360}{\sqrt{18}}$:

   • First, simplify $\sqrt{18}$. It can be written as $\sqrt{9 \times 2} = 3\sqrt{2}$, so: $\frac{360}{\sqrt{18}} = \frac{360}{3\sqrt{2}} = \frac{120}{\sqrt{2}}$
   • Multiply the numerator and denominator by $\sqrt{2}$ to rationalize: $\frac{120}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{120\sqrt{2}}{2} = 60\sqrt{2}$

2. Simplifying the second term:

   • The term $\frac{5}{(5 - 3\sqrt{2})^{2023}}$ involves a very large exponent, and it would result in an extremely small number due to the large power of the denominator. The value would approach zero as $2023$ is a very large exponent.

3. Simplifying the third term:

   • Similarly, the third term $\frac{(10 - 6\sqrt{2})^{2024}}{2^{2022}}$ involves extremely large exponents as well. The power of $2024$ will also contribute to a number that tends to be very small, particularly in relation to the denominator $2^{2022}$.

Conclusion:

Given the large exponents in the second and third terms, both will contribute values that approach zero, and the dominant part of the expression is the first term, which is $60\sqrt{2}$.

Thus, the value of $c$ is approximately: $c \approx 60\sqrt{2}$

Would you like to delve deeper into any part of this solution? Or do you have other questions?

Related questions:

1. How do you rationalize square roots in fractions?
2. What happens when you have large exponents in a fraction?
3. How do you approximate very small values in expressions with large exponents?
4. Can you explain how to simplify an expression with multiple square roots?
5. How do you estimate the magnitude of a number with an exponent like $2024$?

Tip: When dealing with large exponents, often the value becomes so small that it can be approximated as zero in practical calculations.