We can solve this question using matching operations

Given:
Quantity A: 10^7
Quantity B: 7^10

Divide both quantities by 7^7 to get;
Quantity A: (10^7)/(7^7)
Quantity B: (7^10)/(7^7)

Simplify to get;
Quantity A: (10/7)^7
Quantity B: 7^3

ASIDE: If you're wondering how I got (10/7)^7 for Quantity A, I used a nice rule that says (b^x)/c^x) = (b/c)^x

Evaluate 7^3 to get;
Quantity A: (10/7)^7
Quantity B: 343

First recognize that 2^7 = 128
Since 10/7 is LESS THAN 2, we can conclude that (10/7)^7 is some number less than 128
So we have:
Quantity A: some number less than 128
Quantity B: 343

Answer: B

Cheers,
Brent