Given log₂ x = m and log₅ y = n.

(i) Express 2^{m - 3} in terms of x.

(ii) Express 5^{3n + 2} in terms of y.

Given,

⇒ log₂ x = m and log₅ y = n

⇒ x = 2^m ……(1)

and,

⇒ y = 5ⁿ …….(2)

(i) Given,

⇒ 2^{m - 3}

⇒ 2^m.2^-3

⇒ $\dfrac{2^m}{2^3}$

Substituting value of x from equation (1) in above equation, we get :

⇒ $\dfrac{x}{8}$.

Hence, 2^{m - 3} = $\dfrac{x}{8}$.

(ii) Given,

⇒ 5^{3n + 2}

⇒ (5ⁿ)³.5²

Substituting value of 5ⁿ from equation (2) in above equation, we get :

⇒ 25y³

Hence, 5^{3n + 2} = 25y³.