The value of (\(\frac{2}{5}\))-3 × (\(\frac{25}{4}\))-2 =A) \(\frac

1.	The value of (\(\frac{2}{5}\))-3 × (\(\frac{25}{4}\))-2 =A) \(\frac{-5}{2}\)B) \(\frac{-2}{5}\)C) \(\frac{5}{2}\)D) \(\frac{2}{5}\)
Answer» Correct option is (D) 2/5 \((\frac{2}{5})^{-3}\times(\frac{25}{4})^{-2}\) \(=(\frac{2}{5})^{-3}\times(\frac{5^2}{2^2})^{-2}\) \(=((\frac52)^{-1})^{-3}\times((\frac{5}{2})^2)^{-2}\) \(=(\frac52)^{-1\times-3}\times(\frac{5}{2})^{2\times-2}\) \(=(\frac52)^{3}\times(\frac{5}{2})^{-4}\) \(=(\frac52)^{3-4}\) \(=(\frac52)^{-1}\) = \(\frac{2}{5}\) Correct option is D) \(\frac{2}{5}\)

The value of (\(\frac{2}{5}\))-3 × (\(\frac{25}{4}\))-2 =A) \(\frac{-5}{2}\)B) \(\frac{-2}{5}\)C) \(\frac{5}{2}\)D) \(\frac{2}{5}\)

Answer»

Correct option is (D) 2/5

\((\frac{2}{5})^{-3}\times(\frac{25}{4})^{-2}\) \(=(\frac{2}{5})^{-3}\times(\frac{5^2}{2^2})^{-2}\)

\(=((\frac52)^{-1})^{-3}\times((\frac{5}{2})^2)^{-2}\)

\(=(\frac52)^{-1\times-3}\times(\frac{5}{2})^{2\times-2}\)

\(=(\frac52)^{3}\times(\frac{5}{2})^{-4}\)

\(=(\frac52)^{3-4}\)

\(=(\frac52)^{-1}\)

= \(\frac{2}{5}\)

Correct option is D) \(\frac{2}{5}\)