How does the powerlaw ( aN^b ) relate to a log-log run time ( lg(T(N)) = b lg N + c )?

Time Complexity question

The following data is given for the run time of a program: 
https://d2gne97vdumgn3.cloudfront.net/api/file/XF3gUiIRRh2321KcJHbO


And then is graphed in a log-log scale graph and through compressing it for a log-log scale graph, 
has a slope of 3. 
https://d2gne97vdumgn3.cloudfront.net/api/file/n3GlkRKWSg6V1EyKAzOj

The formula for the line can then be described as:
log(T(N)) = b lg N + c

where b is the slope of the line (in this case '3') and c is the value of y 
when the line's the x-axis value is 0. 
(To clarify when x = 0, y = -33.2103)

What I don't understand is how the powerlaw relates back to this? In this example I'm given, 
they use the power law (aNb) for regression and then somehow get the running time of 
1.006 * 10-10 * N^3.

I'm wondering how on earth did they come up with that run time from the formula for T(N)? 

This is the entire slide: http://i.imgur.com/biJt5TK.png 
Please let me know if I need to provide any clarification.