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The equation you've provided is:

\[
81 = 9^{3x}
\]

### Solution:

1. **Express both sides with the same base:**

   Notice that both 81 and 9 are powers of 3. We can rewrite 81 as \(3^4\) and 9 as \(3^2\):

   \[
   3^4 = (3^2)^{3x}
   \]

2. **Simplify the right-hand side:**

   Using the power of a power rule \((a^m)^n = a^{m \cdot n}\):

   \[
   3^4 = 3^{6x}
   \]

3. **Since the bases are the same, we can equate the exponents:**

   \[
   4 = 6x
   \]

4. **Solve for \(x\):**

   \[
   x = \frac{4}{6} = \frac{2}{3}
   \]

Thus, the solution is:

\[
x = \frac{2}{3}
\]

Would you like further details or clarifications?

### Related Questions:
1. How do you solve exponential equations with different bases?
2. What is the general method for solving equations of the form \( a^x = b^y \)?
3. How can logarithms be used to solve equations like \( a = b^{cx} \)?
4. How would you solve \( 2^x = 8 \)?
5. What are the properties of exponents that help simplify expressions?

### Tip:
Always try to express both sides of an exponential equation using the same base to simplify the solving process.

Learn how to solve the exponential equation 81 = 9^(3x) by expressing both sides with the same base and simplifying the exponents. This step-by-step solution is suitable for students in Grades 9-11, covering core algebraic concepts like properties of exponents and exponential equations.

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