Please Explain $\lg(T(N)) = 3 \lg N + \lg a$ is equivalent to $ T(N) = aN^3$

Please Explain $\lg(T(N)) = 3 \lg N + \lg a$ is equivalent to $ T(N) = aN^3$

I'm reading Algorithms by Kevin Wayne and Robert Sedgewick.
They state that:
$\lg(T(N)) = 3 \lg N + \lg a $
(where $a$ is constant) is equivalent to
$T(N) = aN^3$
I know that $\lg$ means a base $10$ logarithm and that $\lg(T(N))$ means
the index of the power to which $10$ must be raised to produce $T(N)$ but
I'd like some help understanding how to get from the first equation to the
second.