https://file.aiquickdraw.com/mathbot/file/1725724260084ec93qsg2.jpg

The equation shown in the image is:

\[
4^{18} = \frac{2^x}{32}
\]

To solve for \(x\), let's follow these steps:

1. **Rewrite the powers of 4 and 32** in terms of base 2:
   \[
   4 = 2^2 \quad \text{so} \quad 4^{18} = (2^2)^{18} = 2^{36}
   \]
   Also,
   \[
   32 = 2^5
   \]
   So the equation becomes:
   \[
   2^{36} = \frac{2^x}{2^5}
   \]

2. **Simplify the right-hand side** by subtracting exponents:
   \[
   \frac{2^x}{2^5} = 2^{x-5}
   \]
   Now the equation is:
   \[
   2^{36} = 2^{x-5}
   \]

3. **Set the exponents equal** (since the bases are the same):
   \[
   36 = x - 5
   \]

4. **Solve for \(x\)**:
   \[
   x = 36 + 5 = 41
   \]

Thus, the solution is:
\[
x = 41
\]

Would you like more details on any step or further clarifications?

Here are some related questions to explore:

1. How would the solution change if the base of the exponent were different (e.g., \(3^{18}\))?
2. What is the general process for solving exponential equations with different bases?
3. Can you solve \(4^x = \frac{2^5}{64}\)?
4. How do you simplify complex exponential expressions like \((2^3)^4\)?
5. How do logarithms help in solving exponential equations?

**Tip**: Always try to express all terms in an exponential equation with the same base to simplify the solving process.

Learn how to solve the exponential equation 4^18 = 2^x / 32 with a step-by-step solution. This problem explores key concepts in exponents and powers, making it suitable for students in Grades 9-12.

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