Drift that makes the tenth power of W a martingale

Let $W_t$ be standard Brownian motion and $a_t$ an adapted process, and consider $X_t=W_t^{10}-\displaystyle\int_0^t a_u\,du$ (the integral uses a dummy variable $u$). The choice of $a_t$ that turns $X_t$ into a martingale has the form $a_t=AW_t^B$ for constants $A$ and $B$. Compute the product $AB$.

$360$. By Ito's formula $d(W_t^{10})=10W_t^9\,dW_t+\tfrac12\cdot90W_t^8\,dt$, so the drift of $X_t$ is $45W_t^8-a_t$. Cancelling it needs $a_t=45W_t^8$, so $A=45$, $B=8$ and $AB=360$.