A woman labels the squares of a very large chessboard 1 through 64. On each square k, the woman puts 2^k grains of rice. How many more grains of rice are placed on the \(10^{th}\) square than on the first 8 squares combined?

On the first 8 squares we have

2^1 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 =

2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 =

510 grains (1)

On the 10th square we have 2^10 = 1024 grains (2)

Subtract (2) - (1) for your answer