Evaluate each of the following:(i) ∛(0.027/0.008) ÷ ∛(0.09/0.04)

1.	Evaluate each of the following:(i) ∛(0.027/0.008) ÷ ∛(0.09/0.04) – 1(ii) ∛(0.1×0.1×0.1×13×13×13)
Answer» (i) ∛(0.027/0.008) ÷ √(0.09/0.04) – 1 = ∛(0.3×0.3×0.3/0.2×0.2×0.2) ÷ √(0.3×0.3/0.2×0.2) = (∛(0.3)³ / ∛(0.2)³) ÷ (√(0.3)² / √(0.2)²) = (0.3/0.2) ÷ (0.3/0.2) -1 = (0.3/0.2 × 0.2/0.3) -1 = 1 – 1 = 0 (ii) ∛(0.1×0.1×0.1×13×13×13) = ∛(0.1³×13³) = 0.1 × 13 = 1.3

Evaluate each of the following:(i) ∛(0.027/0.008) ÷ ∛(0.09/0.04) – 1(ii) ∛(0.1×0.1×0.1×13×13×13)

Answer»

(i) ∛(0.027/0.008) ÷ √(0.09/0.04) – 1

= ∛(0.3×0.3×0.3/0.2×0.2×0.2) ÷ √(0.3×0.3/0.2×0.2)

= (∛(0.3)³ / ∛(0.2)³) ÷ (√(0.3)² / √(0.2)²)

= (0.3/0.2) ÷ (0.3/0.2) -1

= (0.3/0.2 × 0.2/0.3) -1

= 1 – 1

= 0

(ii) ∛(0.1×0.1×0.1×13×13×13)

= ∛(0.1³×13³)

= 0.1 × 13

= 1.3