To simplify the expression \((y^{-5})^4 \times (4^{11})^4\), follow these steps:

1. **Simplify each component separately:**

   \((y^{-5})^4\):

   Use the power rule \((a^m)^n = a^{mn}\):
   \[
   (y^{-5})^4 = y^{-5 \times 4} = y^{-20}
   \]

   \((4^{11})^4\):

   Again, use the power rule \((a^m)^n = a^{mn}\):
   \[
   (4^{11})^4 = 4^{11 \times 4} = 4^{44}
   \]

2. **Combine the simplified components:**

   The expression now looks like:
   \[
   y^{-20} \times 4^{44}
   \]

Since there are no like terms to combine further, the final simplified expression is:
\[
y^{-20} \times 4^{44}
\]

Would you like details or have any questions?

Here are 5 relative questions to expand on this topic:

1. How do you simplify \((x^3)^{-2} \times (2^5)^3\)?
2. What is the value of \(4^{44}\) when evaluated numerically?
3. How do you convert \(y^{-20}\) to a fraction?
4. Can you explain the power rule in more detail?
5. How do you simplify \((z^{-2})^5 \times (3^4)^2\)?

**Tip:** Always remember that when raising a power to another power, you multiply the exponents.

The query submitted by the user: (y^–5)^4×(4^11)^4

Discover how to simplify the expression (y^–5)^4 × (4^11)^4 by applying exponent rules. This problem explores key algebraic concepts such as exponentiation and algebraic simplification, making it suitable for students in Grades 8-10.

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