[tex]\\ \sf\longmapsto \dfrac{(0.0225)^{\frac{-3}{2}}\times (0.0001)^{\frac{3}{4}}}{(0.0125)^{\frac{1}{3}}}[/tex]
[tex]\\ \sf\longmapsto \dfrac{((0.15)^2)^{\frac{-3}{2}}\times ((0.1)^4)^{\frac{3}{4}}}{(0.5)^3)^{\frac{1}{3}}}[/tex]
[tex]\\ \sf\longmapsto \dfrac{(0.15)^{2\times \dfrac{-3}{2}}\times (0.1)^{4\times \dfrac{3}{4}}}{(0.5)^{3\times \dfrac{1}{3}}}[/tex]
[tex]\\ \sf\longmapsto \dfrac{(0.15)^{-3}(0.1)^3}{(0.5)^1}[/tex]
[tex]\\ \sf\longmapsto \dfrac{\dfrac{1}{(0.15)^3}\times 0.001}{0.5}[/tex]
[tex]\\ \sf\longmapsto \dfrac{\dfrac{1}{0.003375}(0.001)}{0.5}[/tex]
[tex]\\ \sf\longmapsto\dfrac{ \dfrac{1000000}{3375}\times \dfrac{1}{1000}}{0.5}[/tex]
[tex]\\ \sf\longmapsto \dfrac{\dfrac{1000}{3375}}{0.5}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1000}{3375}\times \dfrac{10}{5}[/tex]
[tex]\\ \sf\longmapsto \dfrac{2000}{3375}[/tex]
[tex]\\ \sf\longmapsto 0.592[/tex]
The solution to evaluation of the given fraction expression is;
0.592
We want to simplify the expression;
[tex]\frac{0.0225^{-3/2} * 0.0001^{3/4}}{0.0125^{1/3}}[/tex]
Now, we can express each value as;
[tex]0.0225^{-3/2} = (0.15^{2})^{-3/2} \\\\0.0001^{3/4}} = (0.1^{4})^{3/4}\\\\{0.0125^{1/3}} = (0.5^{3})^{1/3}\\[/tex]
Thus, when we simplify each again, we will get;
[tex](0.15^{2})^{-3/2} = (0.15^{-3}) = \frac{1}{0.15^{3}} = \frac{1}{0.003375} \\\\(0.1^{4})^{3/4} = (0.1^{3}) = 0.001\\\\(0.5^{3})^{1/3} = 0.5\\[/tex]
This can be further simplified as;
[tex]\frac{1}{0.003375} = \frac{1000000}{3375} \\\\0.001 = \frac{1}{1000} \\\\0.5 = \frac{5}{10}\\[/tex]
Plugging these into the main equation form gives;
[tex]\frac{\frac{1000000}{3375} * \frac{1}{1000}}{\frac{5}{10}}[/tex]
This will reduce to;
(1000/3375) × (10/5)
⇒ 0.592
Read more on simplification of fraction at; https://brainly.com/question/6109670
