Question

What is `(2^(x+4) - 2(2^x))/(2*(2^(x+3))`?

Answer 1

I found `1/8`

Explanation:

Here we can use a wide collection of rules of exponents such as:
`2^x*2^y=2^(x+y)`
`2^x/2^y=2^(x-y)`
and write it as:
`(2^(x+4)-2^1*2^x)/(2^1*2^(x+3))=`
`=(2^(x+4)-2^(x+1))/(2^(x+3+1))=`
`=(2^(x+4)-2^(x+1))/(2^(x+4))=`
you can write:
`=2^(x+4)/(2^(x+4))-(2^(x+1))/(2^(x+4))=`
use the second property to write:
`=2^(x+4-x-4)-2^(x+1-x-4)=`
`=2^0-2^-3=1-1/2^3=1-1/8=7/8`