Simplify : \((100)^\frac12\times(0.001)^\frac13-(0.0016)^\frac14\time

1.	Simplify : \((100)^\frac12\times(0.001)^\frac13-(0.0016)^\frac14\times3^0+(\frac{5}{4})^{-1}\)
Answer» Given exp. = (10²)^\(\frac12\) x \((\frac{1}{1000})^\frac13-(\frac{16}{1000})^\frac14\times3^0+(\frac54)^{-1}\) = 10^{2 x}^\(\frac12\) x \((\frac{1}{10})^{3\times\frac13} - (\frac{2}{10})^{4\times\frac14}\times3^0+\frac45\) = 10 x \(\frac{1}{10}-\frac15+\frac45\) = 10 × 0.1 – 0.2 + 0.8 = 1 + 0.6 = 1.6.

Simplify : \((100)^\frac12\times(0.001)^\frac13-(0.0016)^\frac14\times3^0+(\frac{5}{4})^{-1}\)

Answer»

Given exp. = (10²)^\(\frac12\) x \((\frac{1}{1000})^\frac13-(\frac{16}{1000})^\frac14\times3^0+(\frac54)^{-1}\)

= 10^{2 x}^\(\frac12\) x \((\frac{1}{10})^{3\times\frac13} - (\frac{2}{10})^{4\times\frac14}\times3^0+\frac45\)

= 10 x \(\frac{1}{10}-\frac15+\frac45\) = 10 × 0.1 – 0.2 + 0.8 = 1 + 0.6 = 1.6.