Simplify :\(\frac{(6.25)^{\frac12}\times(0.0144)^{\frac12}+1}{(0.027)^

1.	Simplify :\(\frac{(6.25)^{\frac12}\times(0.0144)^{\frac12}+1}{(0.027)^{\frac13}\times(81)^{\frac14}}\)(a) 0.14 (b) 1.4 (c) 1 (d) \(1.\overline4\)
Answer» (d) \(1.\overline4\) Given exp. = \(\frac{\big((2.5)^2\big)^{\frac12}\times\big((0.12)^2\big)^{\frac12}+1}{\big((0.3)^3\big)^{\frac13}\times\big((3^4)\big)^{\frac14}}\) = \(\frac{2.5\times0.12+1}{0.3\times3}\) = \(\frac{0.3+1}{0.9} = \frac{1.3}{0.9}=\frac{13}{9}\) = \(1.\overline4\)

Simplify :\(\frac{(6.25)^{\frac12}\times(0.0144)^{\frac12}+1}{(0.027)^{\frac13}\times(81)^{\frac14}}\)(a) 0.14 (b) 1.4 (c) 1 (d) \(1.\overline4\)

Answer»

(d) \(1.\overline4\)

Given exp. = \(\frac{\big((2.5)^2\big)^{\frac12}\times\big((0.12)^2\big)^{\frac12}+1}{\big((0.3)^3\big)^{\frac13}\times\big((3^4)\big)^{\frac14}}\)

= \(\frac{2.5\times0.12+1}{0.3\times3}\)

= \(\frac{0.3+1}{0.9} = \frac{1.3}{0.9}=\frac{13}{9}\) = \(1.\overline4\)