Apply the properties of integer exponents to generate equivalent expressions to 2^/2^-4 with only positive exponents then solve the expression, provides a solution as a whole number
To generate equivalent expressions with only positive exponents, we can use the property of negative exponents, which states that \(a^{-b} = \frac{1}{a^b}\).
Applying this property to \(2^{-4}\), we get:
\(2^{-4} = \frac{1}{2^4}\)
Therefore, our expression \(2^{1/2^{-4}}\) can be rewritten as:
\(2^{1/2^{-4}} = 2^1 \cdot \frac{1}{2^4}\)
Simplifying further:
\(2^1 \cdot \frac{1}{2^4} = 2 \cdot \frac{1}{16} = \frac{2}{16} = \frac{1}{8}\)
So the solution to the expression \(2^{1/2^{-4}}\) with positive exponents is \(\frac{1}{8}\).