Question

Apply the Properties of Integer Exponents to generate equivalent expressions to 2 to the power of 2/2 to the power of −4
with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
2 to the power of 2/2 to the power of −4=

Answer 1

To simplify the expression \( \frac{2^2}{2^{-4}} \) while ensuring all exponents are positive, we can apply the properties of exponents.

1. **Using the Quotient Rule**: The Quotient Rule states that \( \frac{a^m}{a^n} = a^{m-n} \).

\[
\frac{2^2}{2^{-4}} = 2^{2 - (-4)} = 2^{2 + 4} = 2^6
\]

Now, we have \( 2^6 \).

2. **Calculating \( 2^6 \)**:

\[
2^6 = 64
\]

Thus, the equivalent expression is \( 2^6 \), and the solution to the expression \( \frac{2^2}{2^{-4}} \) is:

\[
\boxed{64}
\]