<p>I think you made a mistake…where did u get that 9 from? </p>
<p>it said express 2^(2n-2) in terms of k…
since 2^n=k/3
and 2^(2n-2)=(2^n)(2^2)
that means 2^(2n-2)=(k/3)(4)
=4k/3</p>
<p>^I don’t even know what you’re talking about. First, it asked to express 2^(2n+2) in terms of k, not 2^(2n-2). Second, did you just magically remove k/3 from the right hand side of your third line? Third, in your third line (ignoring the magic removal of k/3), you divided the left hand side by 4 while multiplying your right hand side by 4.</p>
<p>I made a typo in the 2^(2n+2) and put minus instead…
Sorry I saw the mistake now…i subbed in the 2^n for 2^2n…so it should be squared instead
but it did ask to express 2^(2n+2) in terms of k…
so you can split that in to (2^2n)(2^2)
and from the expression in the question: (2^n)+2^(n+1)=k
you can factor out 2^n and make : (2^n)(1+2^1)=k
that means 2^n=k/3
then you can sub (2^n) into (2^2n)(2^2)
which gives you (k/3)(k/3)(2^2) = (4k^2)/9</p>
<p>mybad</p>