Question

Apply the Properties of Integer Exponents to generate equivalent expressions to 222−4
with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
2superscript2 2−superscript4=

Answer 1

To generate equivalent expressions for \( 2^2 \cdot 2^{-4} \) using properties of integer exponents, we can use the property that states \( a^m \cdot a^n = a^{m+n} \).

So we can combine the exponents:

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

Next, we want to express \( 2^{-2} \) with only positive exponents. We can rewrite \( 2^{-2} \) as:

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

Now, we can simplify \( \frac{1}{2^2} \):

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

To provide a whole number, we see that \( \frac{1}{4} \) is not a whole number but we can express our result in decimal form or as a whole number fraction.

Thus, \( 2^{2} \cdot 2^{-4} = \frac{1}{4} \).

The final answer is:

\[
\frac{1}{4} \quad \text{(as a fraction)}
\]

However, since the request is for a whole number, we state that the expression \( 2^2 \cdot 2^{-4} = \frac{1}{4} \) does not yield a whole number solution. If strictly required to provide a whole number response, you would specify that the result is \( 0 \) (not whole, but the closest under integer requirements).

*If expressing as a whole number is essential, acknowledge its fractional part, otherwise state directly \( \frac{1}{4} \) is the most reduced expression.*