The expression \((11x)^4\) can be simplified by applying the power of a product rule. This rule states that \((ab)^n = a^n \cdot b^n\).

So for \((11x)^4\), we apply the exponent to both 11 and \(x\):

\[
(11x)^4 = 11^4 \cdot x^4
\]

Now, calculate \(11^4\):

\[
11^4 = 11 \times 11 \times 11 \times 11 = 14641
\]

Thus, the expression simplifies to:

\[
(11x)^4 = 14641x^4
\]

Would you like further details or have any questions?

Here are 5 related questions for you:
1. How would you simplify \((5x)^3\)?
2. What happens if you square the expression \((11x)^2\)?
3. Can you apply the same exponent rule to \((3x^2y)^3\)?
4. How would you calculate \((2a^3b)^4\)?
5. What is the result of \((4x + 5y)^2\)?

**Tip**: Always apply the exponent to both constants and variables separately when simplifying expressions like \((ab)^n\).

Learn how to simplify the exponential expression (11x)^4 using the power of a product rule. This step-by-step guide covers essential algebraic concepts, including how to apply exponents to constants and variables. Ideal for students in Grades 8-10.

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