x = $2^p$ , y = $2^q$
(a) Express in terms of x and/or y,
(i) $2^{p + q}$
(ii) $2^{2q}$
(iii) $2^{p -1}$
My Working Out:
(i) x + $√y$ because $2^p$ is equal to x and I think $√2^q$ is equal to q
However, I have no idea how to do (ii) or (iii)
I thought maybe (ii) could be $y^2$ but wouldn't that be $(2^q)^2$ which is $4^q$ $^2$.
Thank You and Help is appreciated.
I suspect you mistyped.
For $(i)$, assuming you meant $2^{p+q}$, the answer is $xy$, since $a^b\times a^c=a ^{b+c}$
For $(ii)$, assuming you meant $2^{2q}$, the answer is $y^2$ just as you thought, since $\left(a^b\right)^c=a^{bc}$.
For $(iii)$, (which I think you typed correctly), the answer is $\frac {x}2$ since $\frac 12=2^{-1}$ and $2^{-1}\times 2^p=2^{p-1}$.