Algebraic expressions are expressions that use numbers and variables
The value of A is 65/64
<h3>How to determine the value of A</h3>
The expression is given as:
![2^{x - 6} + 2^x](https://tex.z-dn.net/?f=2%5E%7Bx%20-%206%7D%20%2B%202%5Ex)
Rewrite the expression as:
![2^{x - 6} + 2^x = \frac{2^x}{2^6} + 2^x](https://tex.z-dn.net/?f=2%5E%7Bx%20-%206%7D%20%2B%202%5Ex%20%3D%20%5Cfrac%7B2%5Ex%7D%7B2%5E6%7D%20%2B%202%5Ex)
Factor out 2^x
![2^{x - 6} + 2^x = 2^x(\frac{1}{2^6} + 1)](https://tex.z-dn.net/?f=2%5E%7Bx%20-%206%7D%20%2B%202%5Ex%20%3D%202%5Ex%28%5Cfrac%7B1%7D%7B2%5E6%7D%20%2B%201%29)
Rewrite as product
![2^{x - 6} + 2^x = 2^x * (\frac{1}{2^6} + 1)](https://tex.z-dn.net/?f=2%5E%7Bx%20-%206%7D%20%2B%202%5Ex%20%3D%202%5Ex%20%2A%20%28%5Cfrac%7B1%7D%7B2%5E6%7D%20%2B%201%29)
The expression to compare with is given as: A * 2^x.
So, we have:
![A * 2^x =2^x * (\frac{1}{2^6} + 1)](https://tex.z-dn.net/?f=A%20%2A%202%5Ex%20%20%3D2%5Ex%20%2A%20%28%5Cfrac%7B1%7D%7B2%5E6%7D%20%2B%201%29)
Divide both sides by 2^x
![A =\frac{1}{2^6} + 1](https://tex.z-dn.net/?f=A%20%3D%5Cfrac%7B1%7D%7B2%5E6%7D%20%2B%201)
Take LCM
![A =\frac{1 + 2^6}{2^6}](https://tex.z-dn.net/?f=A%20%3D%5Cfrac%7B1%20%2B%202%5E6%7D%7B2%5E6%7D)
![A =\frac{65}{64}](https://tex.z-dn.net/?f=A%20%3D%5Cfrac%7B65%7D%7B64%7D)
Hence, the value of A is 65/64
Read more about expressions at:
brainly.com/question/4344214