Question

What is the value of AAA when we rewrite 2^{x-6}+2^{x}2 x−6 +2 x 2, start superscript, x, minus, 6, end superscript, plus, 2, start superscript, x, end superscript as A\cdot 2^{x}A⋅2 x A, dot, 2, start superscript, x, end superscript ?

Answer 1

Answer:

$A=\frac{65}{64}\ or\ A=1.015625$

Step-by-step explanation:

Given:

The expression is given as:

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

The equivalent expression to the above expression is given as:

$A\cdot 2^{x}$

Now, simplifying the original expression using the law of indices:

$a^{m-n}=\frac{a^m}{a^n}$

So, $2^{x-6}=\frac{2^x}{2^6}$. The expression becomes:

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

Now, $2^x$ is a common factor to both the terms, so we factor it out. This gives,

$=2^x(\dfrac{1}{2^6}+1)\\\\=2^x(\frac{1}{64}+1)\\\\=2^x(\frac{1}{64}+\frac{64}{64})\\\\=2^x(\frac{1+64}{64})\\\\=2^x(\frac{65}{64})\\\\=(\frac{65}{64})\cdot 2^x$

Now, on comparing the simplified form with the equivalent expression, we conclude:

$A\cdot2^x=(\frac{65}{64})\cdot 2^x\\\\A=\frac{65}{64}\ or\ 1.015625$

Therefore, the value of 'A' is $A=\frac{65}{64}\ or\ A=1.015625$

Answer 2

Answer:

A = 64/65

Step-by-step explanation: