To simplify the expression \(-5x^{-4}\) for \(x = 4\), follow these steps:

1. Substitute \(x = 4\) into the expression:
   \[
   -5(4)^{-4}
   \]

2. Apply the negative exponent rule, which states \(a^{-n} = \frac{1}{a^n}\):
   \[
   -5 \times \frac{1}{4^4}
   \]

3. Calculate \(4^4\) (which is 4 multiplied by itself 4 times):
   \[
   4^4 = 256
   \]

4. Now substitute this into the expression:
   \[
   -5 \times \frac{1}{256} = -\frac{5}{256}
   \]

So, the simplified expression is:
\[
-\frac{5}{256}
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Simplify \(-3x^{-2}\) when \(x = 5\).
2. Simplify \(2x^{-3}\) when \(x = 2\).
3. Simplify \( -6x^{-5} \) for \(x = 3\).
4. Evaluate \( 4x^{-2} \) for \(x = 7\).
5. Find the value of \(x^{-1}\) for \(x = 10\).

**Tip**: When simplifying negative exponents, remember that \(a^{-n} = \frac{1}{a^n}\).

Simplify the expression for x = 4: -5x^-4

This guide shows how to simplify the expression -5x^-4 when x = 4, using the negative exponent rule. Follow step-by-step instructions to calculate 4^4 and solve the expression as -5/256. This problem is ideal for students in Grades 9-10 learning about exponents and negative powers.

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