Given, 2 7 9 We need to simplify the given expression. 2 7 9 = 25 9 = 5 2 3 2 = 5 3 = 1 2 3 Hence, the required answer is 1 2 3 .

Given, 1 9 16 We need to simplify the given expression. 1 9 16 = 25 16 = 5 2 4 2 = 5 4 = 1 1 4 Hence, the required answer is 1 1 4 .

Given, 1728 729 3 We need to evaluate the given expression. = 1728 3 729 3 ∴ a b = a b = ( 12 × 12 × 12 ) 1 3 ( 9 × 9 × 9 ) 1 3 = 12 3 1 3 9 3 1 3 = 12 9 = 4 3 = 1 1 3 Hence, the required answer is 1 1 3 .

Evaluate: 9261 8000 3

Given, 9261 8000 3 We need to evaluate the given expression. = 9261 3 8000 3 ∴ a b = a b = ( 21 × 21 × 21 ) 1 3 ( 20 × 20 × 20 ) 1 3 = 21 3 1 3 20 3 1 3 = 21 20 = 1 1 20 Hence, the required answer is 1 1 20 .

Find the value of 1 2 - 3 .

Given, 1 2 - 3 Using the laws of exponent, 1 a - n = a n Here, a = 2 , n = 3 1 2 - 3 = 2 3 A cube number is found when we multiply a number by itself and then itself again. = 2 × 2 × 2 = 8 Hence, the required answer is 8 .