This is is a lot easier than it looks because each of the terms is a monomial, meaning it is a number (a product) that can be multiplied without reference to the Distributive Law.
(10v^7d) x (4vd^10) x (2v3d^7)
= (40v^8d^11) (6vd^7)
= 240v^9d^18
The only thing strange about the problem is the term 2v3d^7 because that is not the way that term should be written. Canonical form (the way things should be written) dictates that the 2 and 3 should have been multiplied and the term written as 6vd^7. If the problem was mis-copied and the term 2v^3d^7 was intended that would, of course, change the answer.
I will use this problem, a different problem, to demonstrate another way to resolve these expressions.
NOTE DIFFERENT PROBLEM FOR DEMONSTRATION PURPOSES
(10v^7d) x (4vd^10) x (2v^3d^7)
Your coefficients are 10 x 4 x 2 = 80
your exponents for v are 7 + 1 + 3 = 11
your exponents for d are 1+ 10 + 7 = 18
so the combined expression would be 80 v^11 d^18
BUT, again for the problem as submitted, the answer is 240v^9d^18
(10v^7d) x (4vd^10) x (2v3d^7)
= (40v^8d^11) (6vd^7)
= 240v^9d^18
The only thing strange about the problem is the term 2v3d^7 because that is not the way that term should be written. Canonical form (the way things should be written) dictates that the 2 and 3 should have been multiplied and the term written as 6vd^7. If the problem was mis-copied and the term 2v^3d^7 was intended that would, of course, change the answer.
I will use this problem, a different problem, to demonstrate another way to resolve these expressions.
NOTE DIFFERENT PROBLEM FOR DEMONSTRATION PURPOSES
(10v^7d) x (4vd^10) x (2v^3d^7)
Your coefficients are 10 x 4 x 2 = 80
your exponents for v are 7 + 1 + 3 = 11
your exponents for d are 1+ 10 + 7 = 18
so the combined expression would be 80 v^11 d^18
BUT, again for the problem as submitted, the answer is 240v^9d^18
