Question

What is the value of A when we rewrite 2^x-6 + 2x as A * 2^x?

Answer 1

Algebraic expressions are expressions that use numbers and variables

The value of A is 65/64

How to determine the value of A

The expression is given as:

$2^{x - 6} + 2^x$

Rewrite the expression as:

$2^{x - 6} + 2^x = \frac{2^x}{2^6} + 2^x$

Factor out 2^x

$2^{x - 6} + 2^x = 2^x(\frac{1}{2^6} + 1)$

Rewrite as product

$2^{x - 6} + 2^x = 2^x * (\frac{1}{2^6} + 1)$

The expression to compare with is given as: A * 2^x.

So, we have:

$A * 2^x =2^x * (\frac{1}{2^6} + 1)$

Divide both sides by 2^x

$A =\frac{1}{2^6} + 1$

Take LCM

$A =\frac{1 + 2^6}{2^6}$

$A =\frac{65}{64}$

Hence, the value of A is 65/64

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