Question

I want answers of question 15

Answer 1

$\mathrm{Given : \dfrac{\sqrt[3]{\dfrac{0.027}{0.008}}}{\sqrt{\dfrac{0.09}{0.04}}}}$

$\mathrm{\implies \dfrac{{\bigg(\dfrac{0.027}{0.008}\bigg)^{\dfrac{1}{3}}}}{\bigg(\dfrac{0.09}{0.04}\bigg)^{\dfrac{1}{2}}}}}$

●  0.027 = (0.3)³

●  0.008 = (0.2)³

●  0.09 = (0.3)²

●  0.04 = (0.2)²

$\mathrm{\implies \dfrac{{\bigg(\dfrac{(0.3)^3}{(0.2)^3}\bigg)^{\dfrac{1}{3}}}}{\bigg(\dfrac{(0.3)^2}{(0.2)^2}\bigg)^{\dfrac{1}{2}}}}}$

$\mathrm{\implies \dfrac{{\bigg(\bigg(\dfrac{0.3}{0.2}\bigg)^3\bigg)^{\dfrac{1}{3}}}}{\bigg(\bigg(\dfrac{0.3}{0.2}\bigg)^2\bigg)^{\dfrac{1}{2}}}}}$

$\mathrm{\implies \dfrac{{\bigg(\dfrac{0.3}{0.2}\bigg)^{\dfrac{3}{3}}}}{\bigg(\dfrac{0.3}{0.2}\bigg)^{\dfrac{2}{2}}}}}$

$\mathrm{\implies \dfrac{{\bigg(\dfrac{0.3}{0.2}\bigg)}}{\bigg(\dfrac{0.3}{0.2}\bigg)}}}$

$\mathrm{\implies 1}$