Problem A $(30$ points$)$

Consider the equation

$W=\frac{P_{1}V(n-k)}{(k-1)(n-1)}[(\frac{P_{2}sin(2ft-)}{P_1}{)}^{\frac{n-1}{n}}-1]$

where $W$ is work, $V$ is a volume and $t$ is time. Assuming the equation is dimensionally consistent, what are the fundamental dimensions of $P_1,P_2,n,k,f$ and $?$