Find the value of $$(100)^{\frac{1}{2}} \times (0.001)^{\frac{1}{3}} – (0.0016)^{\frac{1}{4}}$$​ ?

Correct option is A

Given:

​$$(100)^{\frac{1}{2}} \times (0.001)^{\frac{1}{3}} - (0.0016)^{\frac{1}{4}} \\$$ 

Concept Used:

$$\begin {array}{|c|c|} \hline \textbf{Operation preference wise} & \textbf{Symbol} \\ \hline Brackets &[],{}, () \\ \hline Orders, of & ² (power), √ (root) , of \\ \hline Division & ÷ \\ \hline Multiplication & × \\ \hline Addition & + \\ \hline Subtraction & - \\ \hline \end{array}$$​

Solution:

​$$\begin{aligned}& (100)^{\frac{1}{2}} = 10 \\& (0.001)^{\frac{1}{3}} = 0.1 \\& (100)^{\frac{1}{2}} \times (0.001)^{\frac{1}{3}} - (0.0016)^{\frac{1}{4}} \\& = 10 \times 0.1 - 0.2 \\& = 1 - 0.2 = 0.8 = \frac{4}{5} \\& \text{Thus, the value is } \frac{4}{5}.\end{aligned}$$​​