Question

Evaluate :$\sqrt{\frac{1}{4}}+{\left(0.01\right)}^{-\frac{1}{2}}-{\left(27\right)}^{{}^{\frac{2}{3}}}$

Answer 1

Given equation is,

$\sqrt{\frac{1}{4}}+(0.01{)}^{-\frac{1}{2}}-{\left(27\right)}^{\frac{2}{3}}$

$=\frac{1}{2}+{\left(\frac{1}{0.01}\right)}^{\frac{1}{2}}-{\left(\right(3{)}^3)}^{\frac{2}{3}}$

$=\frac{1}{2}+\sqrt{\frac{100}{1}}-{\left(\right(3{)}^3)}^{\frac{2}{3}}$

$=\frac{1}{2}+10-{\left(3\right)}^2$

$=\frac{1}{2}+10-9$

$=\frac{3}{2}$

Hence, the value is $\frac{3}{2}$.