use the properties of eponts to simplfy the expresion below -4^-4

To simplify the expression \(-4^{-4}\), we can apply the properties of exponents.

First, recall that \(a^{-n} = \frac{1}{a^n}\). Therefore, we can rewrite \(-4^{-4}\) as:

\[
-4^{-4} = -\frac{1}{(-4)^4}
\]

Next, we calculate \((-4)^4\):

\[
(-4)^4 = (-4) \times (-4) \times (-4) \times (-4) = 16 \times 16 = 256
\]

Now substitute this back into the expression:

\[
-4^{-4} = -\frac{1}{256}
\]

Thus, the simplified expression is:

\[
-\frac{1}{256}
\]

can you say that in a differnt way?

Certainly! Let's simplify \(-4^{-4}\) step-by-step using a different phrasing.

1. **Understanding Negative Exponents**: The expression \(-4^{-4}\) involves a negative exponent. According to the rules of exponents, a negative exponent indicates the reciprocal. So we can rewrite it as follows:

\[
-4^{-4} = -\frac{1}{4^4}
\]

2. **Calculating \(4^4\)**: Now, let's compute \(4^4\). This means multiplying 4 by itself four times:

\[
4^4 = 4 \times 4 \times 4 \times 4 = 16 \times 16 = 256
\]

3. **Substituting the Value**: Now we can plug this value back into our expression:

\[
-4^{-4} = -\frac{1}{256}
\]

So, in simpler terms, we have simplified \(-4^{-4}\) to

\[
-\frac{1}{256}.
\]