To solve the equation \(x^4 = 81\), we follow these steps:

1. Rewrite the equation:
   \[
   x^4 = 81
   \]

2. Take the fourth root of both sides:
   \[
   x = \pm \sqrt[4]{81}
   \]

3. Simplify \(\sqrt[4]{81}\):
   \[
   \sqrt[4]{81} = \sqrt[4]{3^4} = 3
   \]

4. Therefore, the solutions are:
   \[
   x = \pm 3
   \]

So, the solutions to the equation \(x^4 = 81\) are \(x = 3\) and \(x = -3\).

Would you like more details or have any questions?

Here are some questions you might consider asking next:
1. How do you solve \(x^3 = 27\)?
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4. Can you explain how to factor polynomials?
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**Tip:** When solving polynomial equations, always consider all possible roots, including negative and complex roots if applicable.

Learn how to solve the equation x^4 = 81 with a detailed step-by-step solution. This problem involves understanding equations with exponents and roots. Suitable for students in Grades 9-12.

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