Solve the following equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
x6 − 64x4 = 0
x =

The given equation is:

\[
x^6 - 64x^4 = 0
\]

We can factor this equation by factoring out \(x^4\):

\[
x^4(x^2 - 64) = 0
\]

Now, set each factor equal to zero:

1. \(x^4 = 0\)
2. \(x^2 - 64 = 0\)

### Solve \(x^4 = 0\):
\[
x = 0
\]

### Solve \(x^2 - 64 = 0\):
\[
x^2 = 64
\]

Taking the square root of both sides:

\[
x = \pm 8
\]

### Final Answer:
The solutions are \(x = 0, 8, -8\).

\[
x = 0, 8, -8
\]

Would you like a detailed breakdown of any steps? 

Here are 5 related questions to explore this topic further:

1. How would you factor higher-degree polynomials?
2. What is the difference between solving quadratic and cubic equations?
3. How can you solve equations with non-integer exponents?
4. What are some methods to check if your solutions to polynomial equations are correct?
5. How does factoring help in solving complex polynomial equations?

**Tip:** Always start by factoring the simplest terms first to reduce the complexity of polynomial equations!

Solve the following equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) x^6 − 64x^4 = 0

Learn how to solve the polynomial equation x^6 − 64x^4 = 0 by factoring and applying the zero-product property. This algebra problem covers key concepts such as polynomial factoring and square roots. Ideal for Grades 9-11 students.

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