If a b = 9 7 - 3 ÷ 3 7 1 , then find the value of a b 2 .

Given expression is, a b = 9 7 - 3 ÷ 3 7 1 We have to find the value of a b 2 . Using, a b - m = b a m a b = 7 9 3 ÷ 3 7 1 ⇒ a b = 7 9 3 × 7 3 1 ⇒ a b = 7 3 3 2 3 × 7 3 1 Using, a m × a n = a m + n ⇒ a b = 7 3 + 1 3 6 + 1 ⇒ a b = 7 4 3 7 Now, a b 2 = 7 4 3 7 2 = 7 8 3 14 Hence, the value of a b 2 is 7 8 3 14 .

What is the value of: 3 × 2 - 3 .

We need to evaluate: 3 × 2 - 3 Here, 3 × 2 - 3 = 6 - 3 In the power 6 - 3 , we have 6 as the base and the exponent is - 3 . 6 - 3 = 1 6 3 ∵ a - m = 1 a m = 1 6 3 Now, 1 6 is the base and 3 is the exponent. ∴ 1 6 3 = 1 6 × 1 6 × 1 6 = 1 216 Hence, the value of 3 × 2 - 3 is 1 6 3 or 1 216 .

Express with positive exponent: - 4 13 - 6 ÷ - 4 13 - 4

We have, - 4 13 - 6 ÷ - 4 13 - 4 = - 4 13 - 6 - - 4 ∵ a m a n = a m - n = - 4 13 - 6 + 4 = - 4 13 - 2 Positive exponents indicate that a number's power is positive. Since, x y - z = y x z So, - 4 13 - 2 = - 13 4 2 Therefore, the required answer is - 13 4 2 .