If 2 3 6 × 9 4 5 = 3 2 m + 2 , then find the value of m .

Given :- 2 3 6 × 9 4 5 = 3 2 m + 2 3 2 - 6 × 3 2 2 5 = 3 2 m + 2 3 2 - 6 × 3 2 2 × 5 = 3 2 m + 2 ∵ a m n = a m n 3 2 - 6 × 3 2 10 = 3 2 m + 2 3 2 - 6 + 10 = 3 2 m + 2 ∵ a m × a n = a m + n 3 2 4 = 3 2 m + 2 If bases are equal we can compare powers, Therefore, 4 = m + 2 m = 4 - 2 m = 2

Write the rationalizing factor of : 5 - 2 3

Rationalising factor is a term with which a term is multiplied or divided to make the whole term rational. The rationalising factor of a - b is a + b and vice versa. Hence, The Rationalising factor of 5 - 2 3 is 5 + 2 3 .

Write the rationalizing factor of : 1 x + y

Rationalising factor is a term with which a term is multiplied or divided to make the whole term rational. Hence, 1 x + y rationalising factor is x - y .

If 1 7 = 0.14285 , then find the value of 3 7 .

Given that, 1 7 = 0.14285 Then 3 7 will be, 3 ( 1 7 ) = 3 ( 0 . 14285 ) = 0 . 42855 Therefore, the value of 3 7 is 0.42855 .

If 10 = 3.1622 , then find the value of 1 10 .

Given 10 = 3 . 1622 we have to find value of 1 10 Multiply both numerator and denominator by 10 1 10 × 10 10 = 10 10 Substitute the value of 10 we get, 1 10 = 3 . 1622 10 = 0 . 31622