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

Answer 1

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:

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

Answer 2

can you say that in a differnt way?

Answer 3

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

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