To solve this expression, we can use the rules of exponents.
When we divide two powers with the same base, we subtract their exponents. Therefore, 3^{10}/{3^{5}} = 3^{10-5} = 3^5
Next, we multiply(3^5) by (3^8). When we multiply two powers with the same base, we add their exponents. Therefore, (3^5 times 3^8 = 3^{5+8} = 3^{13}
So, the value that goes in the green box is {13}