Question

use rational exponents to write ^2sqrt5 x ^3sqrt8 as a single radical expression

Answer 1

Do you mean :

$$ \large \huge\sqrt[2]{5} \times \sqrt[3]{8} = ?$$

Answer 2

If yes then the answer is $$2 \sqrt{5}$$

Answer 3

NOTE : $$ \sqrt[2]{5} = \sqrt{5}$$