Find the product sqrt 5 * ^3 sqrt 5 (see picture)

For this case, what you should know is that for the same base the exponents are added.
 We have then:
 base = 5
 Exponents = (1/2) and (1/3)
 Solving the product we have:
 (sqrt 5) * (^ 3 sqrt 5) = 5 ^ ((1/2) + (1/3)) = 5 ^ (5/6)
 answer
 (sqrt 5) * (^ 3 sqrt 5) = 5 ^ (5/6)