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The equation you've provided is:

\[
3^8 : x = 3^8
\]

This can be interpreted as a division equation, where \(3^8 : x\) is another way of writing \( \frac{3^8}{x} \).

Let's solve this step by step:

1. Start with the equation:
   \[
   \frac{3^8}{x} = 3^8
   \]

2. Multiply both sides of the equation by \(x\) to isolate the fraction:
   \[
   3^8 = 3^8 \cdot x
   \]

3. Divide both sides by \(3^8\) to solve for \(x\):
   \[
   x = \frac{3^8}{3^8}
   \]

4. Since \( \frac{3^8}{3^8} = 1 \), we find:
   \[
   x = 1
   \]

Thus, the solution is:

\[
x = 1
\]

Would you like further details on any step, or have any questions?

Here are 5 related questions for practice:
1. What is the value of \(3^8\)?
2. How would you solve \(2^5 : y = 2^3\)?
3. What is the solution to the equation \(5^4 : z = 5^4\)?
4. If \(a^b : x = a^c\), how would you solve for \(x\)?
5. Can you solve \(10^3 : y = 10^2\)?

**Tip:** When solving equations involving powers of the same base, use properties of exponents to simplify the process efficiently.

Learn how to solve the equation 3^8 : x = 3^8 step by step using properties of exponents. This problem is suitable for students in Grades 6-8 and involves simplifying powers and solving basic algebraic equations.

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