Fully simplify and write your answer in exponential form with positive exponents only. Example: 153\frac{1}{5^3}

To simplify the expression \(2^{-7} \cdot 2 \cdot 2^{-4}\), we can use the property of exponents which states that when multiplying numbers with the same base, you add their exponents.

Let's rewrite \(2\) as \(2^1\):

\[
2^{-7} \cdot 2^1 \cdot 2^{-4}
\]

Now we can add the exponents:

\[
-7 + 1 - 4 = -10
\]

So, we have:

\[
2^{-10}
\]

Now, to express this with positive exponents, we use the property that \(a^{-n} = \frac{1}{a^n}\):

\[
2^{-10} = \frac{1}{2^{10}}
\]

Thus, the fully simplified form of the expression \(2^{-7} \cdot 2 \cdot 2^{-4}\) in exponential form with positive exponents is:

\[
\frac{1}{2^{10}}
\]