The given expression is:

\[
4u \times 2x^9 \times 2u^9 x^3
\]

We can simplify it by multiplying the constants, combining like terms, and applying the laws of exponents:

1. Multiply the constants: \( 4 \times 2 \times 2 = 16 \).
2. Combine powers of \( u \): \( u^1 \times u^9 = u^{1+9} = u^{10} \).
3. Combine powers of \( x \): \( x^9 \times x^3 = x^{9+3} = x^{12} \).

Thus, the simplified expression is:

\[
16 u^{10} x^{12}
\]

Would you like more details or have any questions about this?

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Here are 5 related questions to expand your understanding:

1. How do you simplify expressions involving multiple variables?
2. What are the laws of exponents used in simplification?
3. How would the expression change if you had division instead of multiplication?
4. Can you simplify \( u^5 \times u^3 \times u^2 \)?
5. What happens if you had negative exponents in the expression?

**Tip:** When multiplying terms with the same base, remember to add their exponents!

Learn how to simplify the algebraic expression 4u * 2x^9 * 2u^9 * x^3 by combining like terms and applying the laws of exponents. This problem is perfect for students in Grades 7-9, covering key concepts like exponent addition and multiplication of variables.

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