You are on the right track. But you should leave the power x outside of the radical (√).

The idea now is to move all the terms with power x to the left.

Based on your working, you could start with :

16ˣ × 25ˣ / 25 = (4³/²)ˣ / 4 × 5ˣ / 5

Then,

16ˣ × 25ˣ / 25 = (√4³)ˣ × 5ˣ / (4×5)
16ˣ × 25ˣ / 25 = (√64)ˣ × 5ˣ / 20
16ˣ × 25ˣ / 25 = 8ˣ × 5ˣ / 20
16ˣ × 25ˣ / (8ˣ × 5ˣ) = 25 / 20
(16 × 25 / (8×5) )ˣ = 5/4
10ˣ = 5/4
(10ˣ)² = (5/4)²
(10²)ˣ = 5²/4²

100ˣ = 25/16




Or you could start with :

16ˣ × 25ˣ / 25 = (4¹/²)³ˣ/ 4 × 5ˣ / 5
16ˣ × 25ˣ / 25 = (√4)³ˣ × 5ˣ / (4 × 5)
16ˣ × 25ˣ / 25 = (2)³ˣ × 5ˣ / 20
16ˣ × 25ˣ / 25 = 8ˣ × 5ˣ / 20


Continue the steps as previously shown above.

b)

100ˣ = 25/16

We can reuse the earlier result :

10ˣ = 5/4
x = lg(5/4) or lg(1.25)

x ≈ 0.0969 (3s.f)