The value of $(0.243{)}^{0.2}\times (10{)}^{0.6}$ is

Let us simplify each part of the expression:
$$(0.243{)}^{0.2}={\left(\frac{243}{1000}\right)}^{\frac{1}{5}}={\left(\frac{3^5}{10^3}\right)}^{\frac{1}{5}}=\frac{3}{10^{3/5}}=\frac{3}{10^{0.6}}$$

Now substitute this back into the original product expression:

$$\frac{3}{10^{0.6}}\times (10{)}^{0.6}=3$$