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

Question

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