Question

Find the reciprocal of the rational number `(1/2)^2 ÷ (2/3)^3`

Answer 1

Given, `(1/2)^2 ÷ (2/3)^3 = (1/2)^2/(2/3)^3`  ......`[∵ a ÷ b = a/b]`

= `((1)^2/(2)^2)/((2)^3/(3)^3)` = `((1/4))/((8/27))`  ......`[∵ (a/b)^n = a^n/b^n]` [∵ 1² = 1, 2² = 4, 2³ = 8 and 3³ = 27]

= `1/4 xx 27/8 = 27/(4 xx 8) = 27/32`  ......`[∵ a/b ÷ c/d = a/b xx d/c]`

We know that, reciprocal of a rational number is obtained by interchanging the numerator and denominator

∴ Reciprocal og given number = `32/27`.