Express - 2 5 3 - 3 in the form p q .

Given, - 2 5 3 - 3 We have to express as a rational number of the form p q . We know that, a - n = 1 a n , a b n = a n b n Now, - 2 5 3 - 3 = - 2 3 5 3 - 3 = - 2 3 5 3 - 3 = 5 3 - 2 3 3 = - 5 9 2 9 Hence, - 2 5 3 - 3 = - 5 9 2 9 .

For which value of p and q the relation p q - m = p q m is not meaningful?

Given relation is p q - m = p q m . We know that, a - n = 1 a n The given relation is meaningful only for p = q . That is, p p - m = p p m ⇒ 1 - m = 1 m ⇒ 1 = 1 Hence, the relation is not meaningful for p ≠ q .

By what number should - 3 2 - 4 be divided so that the quotient may be 4 729 - 2 ?

Let - 3 2 - 4 should be divided by x so that the quotient may be 4 729 - 2 . That is - 3 2 - 4 ÷ x = 4 729 - 2 ⇒ 2 - 3 4 ÷ x = 729 4 2 ⇒ x = 2 - 3 4 ÷ 729 4 2 ⇒ x = 2 - 3 4 × 4 729 2 ⇒ x = 2 4 3 4 × 2 2 3 6 2 ⇒ x = 2 8 3 16 Hence, the answer is 2 8 3 16 .