Question

Simplify: $(100{)}^{\frac{1}{2}}\times (0.001{)}^{\frac{1}{3}}-(0.0016{)}^{\frac{1}{4}}\times 3^0+{\left(\frac{5}{4}\right)}^{-1}$

• A. 1.6
• B. 2.4
• C. 2
• D. 1.4

Answer 1

The correct option is A 1.6

$(100{)}^{\frac{1}{2}}\times (0.001{)}^{\frac{1}{3}}-(0.0016{)}^{\frac{1}{4}}\times 3^0+{\left(\frac{5}{4}\right)}^{-1}$

$=({10}^2{)}^{\frac{1}{2}}\times {\left(\frac{1}{1000}\right)}^{\frac{1}{3}}-{\left(\frac{16}{10000}\right)}^{\frac{1}{4}}\times 3^0+{\left(\frac{5}{4}\right)}^{-1}$

$={10}^{2\times \frac{1}{2}}\times {\left(\frac{1}{10}\right)}^{3\times \frac{1}{3}}-{\left(\frac{2}{10}\right)}^{4\times \frac{1}{4}}\times 3^0+\frac{4}{5}$

$=10\times \frac{1}{10}-\frac{1}{5}+\frac{4}{5}$

$=10\times 0.1-0.2+0.8$

$=1+0.6=1.6$