Express the following number in the exponential form. 121 10000

First, we shall express both the numerator 121 and the denominator 10000 as the product of its prime factors as follows: 11 121 11 11 1 2 10000 2 5000 2 2500 2 1250 5 625 5 125 5 25 5 5 1 Thus, 121 = 11 × 11 = 11 2 and 10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5 = 2 4 5 4 [ x × x × x × x × . . . . . . . n times = x n ] So, 121 10000 = 11 2 2 4 5 4 Therefore, the required answer is 11 2 2 4 5 4 .

Simplify the following: 2 3 × 2 5

We have, 2 3 × 2 5 = 2 3 + 5 ∵ a m × a n = a m + n = 2 8 Therefore, the required answer is 2 8 .

Simplify the following: 9 2 × 3 3

We have, 9 2 × 3 3 = 3 2 2 × 3 3 = 3 2 × 2 × 3 3 ∵ a m n = a m × n = 3 4 × 3 3 = 3 4 + 3 ∵ a m × a n = a m + n = 3 7 Therefore, the required answer is 3 7 .

Simplify the following: 8 13 ÷ 8 7

We have, 8 13 ÷ 8 7 = 8 13 8 7 = 2 3 13 2 3 7 = 2 3 × 13 2 3 × 7 ∵ a m n = a m × n = 2 39 2 21 = 2 39 - 21 ∵ a m a n = a m − n = 2 18 Therefore, the required answer is 2 18 .