Certainly! Let's break down the simplification of [tex]\(4^{-4}\)[/tex] step by step:
1. Understand the Negative Exponent:
A negative exponent indicates that the base should be taken as the reciprocal and the exponent should be made positive. So, [tex]\(4^{-4}\)[/tex] can be rewritten as:
[tex]\[
4^{-4} = \frac{1}{4^4}
\][/tex]
2. Calculate [tex]\(4^4\)[/tex]:
To simplify further, we need to determine what [tex]\(4^4\)[/tex] equals. We can break it down:
[tex]\[
4^4 = 4 \times 4 \times 4 \times 4
\][/tex]
3. Perform the Multiplication:
Let's compute the value of [tex]\(4^4\)[/tex]:
[tex]\[
4 \times 4 = 16
\][/tex]
[tex]\[
16 \times 4 = 64
\][/tex]
[tex]\[
64 \times 4 = 256
\][/tex]
Therefore, [tex]\(4^4 = 256\)[/tex].
4. Determine the Reciprocal:
Now that we know [tex]\(4^4 = 256\)[/tex], we can go back to our expression involving the negative exponent:
[tex]\[
4^{-4} = \frac{1}{4^4} = \frac{1}{256}
\][/tex]
Hence, the simplified form of [tex]\(4^{-4}\)[/tex] is [tex]\(\frac{1}{256}\)[/tex].
The correct answer is:
[tex]\[
\frac{1}{256}
\][/tex]
