Simplify and express each of the following as a rational number :

(i) $\Big(\dfrac{6}{5}\Big)^3 \times \Big(\dfrac{5}{2}\Big)^2$

(ii) $\Big(\dfrac{3}{4}\Big)^2 \times \Big(\dfrac{-1}{2}\Big)^5 \times 2^3$

(iii) $\Big(\dfrac{5}{4}\Big)^2 \times \Big(\dfrac{2}{3}\Big)^2 \times \Big(\dfrac{-3}{5}\Big)^3$

(iv) $\Big(\dfrac{-3}{4}\Big)^3 \times \Big(\dfrac{-5}{2}\Big)^3 \times \Big(\dfrac{2}{3}\Big)^5$

(v) $\Big(\dfrac{7}{11}\Big)^6 ÷ \Big(\dfrac{7}{11}\Big)^3$

(vi) $\Big(\dfrac{-4}{3}\Big)^8 ÷ \Big(\dfrac{-4}{3}\Big)^{12}$

Simplify and express each of the following as a rational number :

(i) $\dfrac{10^2 \times 15^3}{2^2 \times 3 \times 5^5 \times 6^4}$

(ii) $\dfrac{3^5 \times 25 \times 10^5}{5^7 \times 6^5}$

The RAM of a computer is 8 gigabyte. If each gigabyte is equal to 10⁹ bytes, then express the RAM in bytes.

In a tennis competition, 128 players were selected for a series of knockout rounds. In each round the losers were eliminated and the winners reached the next round. How many players moved to the next round after 4th round? Express this number in the exponential notation in terms of the initial number of players.