Given:
[tex](5a^2c^{-\frac{1}{2}}d^{\frac{3}{4}})^2[/tex]
Applying the properties of exponents:
[tex]\begin{gathered} =(5)^2\text{ }\times(c^{-\frac{1}{2}})^2\text{ }\times(d^{\frac{3}{4}})^2 \\ =\text{ 25 }\times c^{-\frac{1}{2}\times2}\text{ }\times d^{\frac{3}{4}\times2} \\ =\text{ 25 }\times c^{\frac{-2}{2}}\times d^{\frac{6}{4}} \\ =\text{ 25 }\times c^{-1}\times d^{\frac{3}{2}} \end{gathered}[/tex]
Simplifying the powers:
[tex]=\text{ 25 }\times c^{-1}\times d^{\frac{3}{2}}[/tex]
Writing exponents as positive integers:
[tex]=\text{ }\frac{25d^{\frac{3}{2}}}{c}[/tex]
The result as a radical expression:
[tex]=\text{ }\frac{25\sqrt[]{d^3}}{c}[/tex]
