Step-by-step explanation:

1.

4/(10)^1/2 × ((10)^1/2)/((10)^1/2) = (4(10)^1/2)/10

=(2 (10)^1/2)/5

2.

3/(5)^1/2 × ((5)^1/2)/((5)^1/2) = (3(5)^1/2)/5

3.

4/(8)^1/2 ×( (8)^1/2)/((8)^1/2) = (4(8)^1/2)/8

=((8)^1/2)/2 = (2(2)^1/2)/2 = (2)^1/2

4.

-4/3(2)^1/2 × ((2)^1/2)/((2)^1/2)

= (-4(2)^1/2)/3(2)

= (-4(2)^1/2)/6

= (-2(2)^1/2)/3

5.

((3)^1/2)/((8)^1/2) × ((8)^1/2)/((8)^1/2)

=((24)^1/2)/8 = (2(6)^1/2)/8 = ((6)^1/2)/4