Partition function, discriminant function modular forms, really just algebra

1. The problem statement, all variables and given/known data

I am wanting to show that $\Delta (t) = 1/q (\sum\limits^{\infty}_{n=0} p(n)q^{n})^{24}$

where $\Delta (q) = q \Pi^{\infty}_{n=1} (1-q^{n})^{24}$ is the discriminant function and $p(n)$ is the partition function,

2. Relevant equations

Euler's result that :

$\sum\limits^{\infty}_{n=0} p(n)q^{n} = \Pi^{\infty}_{n=1} (1-q^{n})^{-1}$


3. The attempt at a solution

To be honest , I'm probably doing something really stupid, but at first sight, I would have thought we need

$\sum\limits^{\infty}_{n=0} p(n)q^{n}$

raised to a negative power, as raising to $+24$ looks like your going to get something like $(1-q^{n})^{-24}$..

. I've had a little play and get the following...

$\Delta (q) = q \Pi^{\infty}_{n=1} (1-q^{n})^{24} = \frac{q \Pi^{\infty}_{n=1}(1-q^{n})^{25}}{\Pi^{\infty}_{n=1}(1-q^{n}})=(\Pi^{\infty}_{n=1} (1-q^{n})^{25}) q \sum\limits^{\infty}_{n=1} p(n) q^{n}$

(don't know whether it's in the right direction or where to turn next..)

Many thanks in advance.