To simplify the given expression:

\[
(5x)^3 - (2x)^2 + (7x)^5 + (x)^6 - 4x + 8
\]

We simplify each term individually:

1. \((5x)^3 = 125x^3\)
2. \((2x)^2 = 4x^2\)
3. \((7x)^5 = 16807x^5\)
4. \((x)^6 = x^6\)
5. The terms \(-4x\) and \(8\) remain as they are.

Now, substituting back:

\[
125x^3 - 4x^2 + 16807x^5 + x^6 - 4x + 8
\]

Rewriting the expression in descending powers of \(x\):

\[
x^6 + 16807x^5 + 125x^3 - 4x^2 - 4x + 8
\]

This is the simplified version of the expression.

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Would you like more details on any specific part of the simplification?

Here are 5 related questions to expand your understanding:
1. How do you simplify exponents when multiplying variables?
2. What happens when you multiply or divide powers with the same base?
3. How do you factor a polynomial expression?
4. Can you find the derivative of this expression?
5. How would you solve this equation if it were equal to zero?

**Tip:** Always group terms by powers of \(x\) to simplify complex polynomials.

(5x)^3 - (2x)^2 + (7x)^5 + (x)^6 - 4x + 8

This article provides a step-by-step guide to simplifying the polynomial expression (5x)^3 - (2x)^2 + (7x)^5 + (x)^6 - 4x + 8. Learn how to handle exponents, simplify terms, and rewrite the expression in descending powers of x. Suitable for high school students in Grades 9-12.

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