Explanation
We are asked to simplify the given question
[tex](\frac{75d^{\frac{18}{5}}}{3d^{\frac{3}{5}}})^{\frac{5}{2}}[/tex]
To simplify the terms, we will follow the steps below
Step 1: simplify the terms in the bracket using the exponential rule
Thus for the terms in the parentheses
[tex](\frac{75d^{\frac{18}{5}}}{3d^{\frac{3}{5}}})=\frac{75}{3}\times d^{\frac{18}{5}-\frac{3}{5}}[/tex]
Hence
[tex]25\times d^{\frac{18-3}{5}}=25d^{\frac{15}{5}}=25d^3[/tex]
Simplifying further
[tex]25d^3=25d^3[/tex]
Step 2: substitute the value obtained above in step 1 into the parentheses, so that
[tex](\frac{75d^{18\/5}}{3d^{3\/5}})^{\frac{5}{2}}=(25d^3)^{\frac{5}{2}}[/tex]
Step 3: Simplify further, we will apply the rule
so that
[tex](25d^3)^{\frac{5}{2}}=25^{\frac{5}{2}}d^{3\times\frac{5}{2}}[/tex]
Simplifying further
[tex]\begin{gathered} we\text{ will have} \\ \sqrt{25^5}\times d^{\frac{15}{2}}=3125d^{\frac{15}{2}} \end{gathered}[/tex]
Hence, our final answer is
[tex]3125d^{\frac{15}{2}}[/tex]
