Question

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

1
​
not 5−35^{-3}5
−3
.



2−6⋅2⋅2−5=2^{-6}\cdot2\cdot2^{-5}=2
−6
⋅2⋅2
−5
=

Answer 1

To simplify the expression \(2^{-6} \cdot 2 \cdot 2^{-5}\), we can use the property of exponents that states \(a^m \cdot a^n = a^{m+n}\).

Let's break it down step by step:

1. Rewrite the expression:
\[
2^{-6} \cdot 2^1 \cdot 2^{-5}
\]

2. Now, combine the exponents. We can add the exponents:
\[
-6 + 1 - 5 = -10
\]

3. This gives us:
\[
2^{-10}
\]

4. Since the problem asks for the answer in exponential form with positive exponents, we convert \(2^{-10}\) to positive exponent form:
\[
2^{-10} = \frac{1}{2^{10}}
\]

Therefore, the fully simplified answer is:
\[
\frac{1}{2^{10}}
\]