# Thread: Simplifying an expression with 2's raised to powers

1. ## Simplifying an expression with 2's raised to powers

Hey people!

$\displaystyle \frac{2^n+^4 - 2.2^n} {2.2^n+^3}$

It's easy?!

I just can't transform those stuffs in numbers !!!

2. Originally Posted by _icebox
Hey people!

$\displaystyle \frac{2^n+^4 - 2.2^n} {2.2^n+^3}$

It's easy?!

I just can't transform those stuffs in numbers !!!

$\displaystyle \frac{2^{n+4} - 2\times2^n} {2.2^{n+3}}$

$\displaystyle a^{x} \times a^{y} = a^{x+y}$

$\displaystyle =\frac{2^{n+4} - 2^{n+1}} {2^{n+4}}$

$\displaystyle =\frac{2^{n+4} - 2^{n+1}} {2^{n+4}}$

Divide numerator and denominator by $\displaystyle 2^{n+1}$

$\displaystyle =\frac{2^{3} - 1} {2^{3}}$

$\displaystyle =\frac{8 - 1} {8}$

$\displaystyle =\frac{7} {8}$

$\displaystyle \frac{2^{n+4} - 2\times2^n} {2.2^{n+3}}$

$\displaystyle a^{x} \times a^{y} = a^{x+y}$

$\displaystyle =\frac{2^{n+4} - 2^{n+1}} {2^{n+4}}$

$\displaystyle =\frac{2^{n+4} - 2^{n+1}} {2^{n+4}}$

Divide numerator and denominator by $\displaystyle 2^{n+1}$

$\displaystyle =\frac{2^{3} - 1} {2^{3}}$

$\displaystyle =\frac{8 - 1} {8}$

$\displaystyle =\frac{7} {8}$
I'm impressed that you could interpret $\displaystyle 2.2^n$ as $\displaystyle 2 \cdot 2^n$.

I was having a tough time fooling around with the decimal.

4. Originally Posted by masters
I'm impressed that you could interpret $\displaystyle 2.2^n$ as $\displaystyle 2 \cdot 2^n$.

I was having a tough time fooling around with the decimal.
The time I saw that + sign jumping up and down , I knew interpretation is the keyword ..

5. Yes! That's it!!!

I've some problems with the Latex... I don't know exacly how to use that hauhauhaha

But that's exacly what I was looking for =D
I stopped when it was necessary to divide numerator and denominator =P