none of the option is correct.
step-by-step explanation:
it says to find which expression equals 9^3 sqrt 10 = ?
9^3 sqrt 10 = 729 sqrt 10.
checking option a. 5 sqrt 10 + 4 sqrt 10
5 sqrt 10 + 4 sqrt 10
= 9 sqrt 10.
checking option b. 5^3 sqrt 10 + 4^3 sqrt 10
5^3 sqrt 10 + 4^3 sqrt 10
= 125 sqrt 10 + 64 sqrt 10
= 189 sqrt 10.
checking option c. 5 sqrt 10 + 4^3 sqrt 10
5 sqrt 10 + 4^3 sqrt 10
= 5 sqrt 10 + 64 sqrt 10
= 69 sqrt 10.
checking option d. 5^3 sqrt 10 + 4 sqrt 10
5^3 sqrt 10 + 4 sqrt 10
= 125 sqrt 10 + 4 sqrt 10
= 129 sqrt 10.
hence, none of the option is correct.