Question

EvaluateUse the rules of exponents to simplify the following expression and remove all zero and negative exponents. Assume that all variables are nonzero.
left parenthesis 2 Superscript negative 1 Baseline right parenthesis Superscript 4
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Part 1
left parenthesis 2 Superscript negative 1 Baseline right parenthesis Superscript 4equals
  
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​(Type an integer or a​ fraction.)

Answer 1

To simplify the expression \((2^{-1})^4\), we apply the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\).

1. Using this rule:

\[
(2^{-1})^4 = 2^{-1 \cdot 4} = 2^{-4}
\]

2. Next, we know that \(2^{-4}\) can be expressed with a positive exponent by using the rule \(a^{-m} = \frac{1}{a^m}\):

\[
2^{-4} = \frac{1}{2^4}
\]

3. Now, we calculate \(2^4\):

\[
2^4 = 16
\]

4. Therefore,

\[
2^{-4} = \frac{1}{16}
\]

So, the fully simplified expression without any zero or negative exponents is:

\[
\frac{1}{16}
\]

Thus, the answer is:

\(\frac{1}{16}\)