Cross Wits With a 7-Year-Old

My son, a math genius much smarter than his father, periodically pesters Papa for puzzles. So yesterday I created for him this CrossNumber puzzle, in which the empty squares must be filled with the proper numerals. I'm proud to report that he solved it on his own, with occasional help from Google. (His mother had removed IE and Flock from his PC as a protective measure, but he has since figured out how to RDP into my PC whenever he needs a browser).

Across
1	(2+7) * (475 - 468)
3	Declaration of Independence
7	(10-1)2 - 12
8	11 in base 3
9	x	÷	x
10	79, in base 8
11	2*x2 = x+1
12	Binary: 110 - 101 = ?
14	Roll dice 72 times. How many 7's?
15	US Route near home
16	The power of Googol
17	Crosses Stanford Linear Accelerator
18	-3, 0, 3, …
Down
1	0, 2, 4, …
2	Days in April
3	Your age, to a computer
4	1st successful commercial jet
5	23 * 32
6	I am my name
10	Emperor Henry V invades Italy
11	Two minutes
13	James Bond's successor
14	Meitnerium
16	Pawns on board

A solution grid is available upon request.