Simplifying an expression with 2's raised to powers

• Mar 18th 2009, 04:39 AM
_icebox
Simplifying an expression with 2's raised to powers
Hey people!

$

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

$

It's easy?!

I just can't transform those stuffs in numbers (Headbang) !!!
• Mar 18th 2009, 05:13 AM
Quote:

Originally Posted by _icebox
Hey people!

$

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

$

It's easy?!

I just can't transform those stuffs in numbers (Headbang) !!!

$

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

$

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

$

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

$

$

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

$

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

$

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

$

$

=\frac{8 - 1} {8}

$

$

=\frac{7} {8}

$
• Mar 18th 2009, 05:22 AM
masters
Quote:

$

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

$

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

$

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

$

$

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

$

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

$

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

$

$

=\frac{8 - 1} {8}

$

$

=\frac{7} {8}

$

I'm impressed that you could interpret $2.2^n$ as $2 \cdot 2^n$.

I was having a tough time fooling around with the decimal.
• Mar 18th 2009, 05:25 AM
Quote:

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

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 :p ..(Giggle)
• Mar 18th 2009, 05:27 AM
_icebox
Yes! That's it!!! (Clapping)

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