$ \left(2^\left(n+3\right) - 2^n\right)/14 $
My thought process behind solving it was to spilt the first 2 term into two separate terms then cancelling the 2^n leaving 2^3 over 14
$ (2^n \cdot 2^3-2^n)/14 $
$ (2^3)/14 = 8/14
$
however this is incorrect, how am i supposed to correctly simplify this equation?
Sorry about messing up the formatting so much
Are you having trouble simplifying this fraction? Well, you have failed to see that you can factor out $2^n$ from the expression in the numerator. What you did there is an incorrect piece of mathematics. Memorize this fact: $ab \pm a=a(b \pm 1)$. The idea here is that if each term in an expression shares a common factor, you can bring it out front. Once you've factored out the $2^n$, the rest is pretty straightforward. Here's how it typically would be done:
$$ \frac{2^{n+3}-2^n}{14}= \frac{2^n\cdot 2^3 - 2^n}{14}= \frac{2^n(2^3 - 1)}{14}= \frac{2^n(8-1)}{14}= \frac{2^n \cdot 7}{14}= \frac{2^n}{2}= 2^n \cdot 2^{-1}= 2^{n-1} $$
And that's as far as you can go in terms of simplification.
Steps:
$2^{n+3}= 2^n2^3= 2^n×8.$
$(2^{n+3} -2^n) = 2^n(8-1)=7×2^n.$
$14=2×7$.
$\dfrac{7×2^n}{14}= 2^n/2^1= 2^{n-1}.$
