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Hello, is it possible to show me the steps to simplify this problem? I don't understand the solution provided in my textbook.

Hello, is it possible to show me the steps to simplify this problem? I don't understand-example-1

1 Answer

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Step-by-step explanation

We are asked to simplify the given question


(\frac{75d^{(18)/(5)}}{3d^{(3)/(5)}})^{(5)/(2)}

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


(\frac{75d^{(18)/(5)}}{3d^{(3)/(5)}})=(75)/(3)* d^{(18)/(5)-(3)/(5)}

Hence


25* d^{(18-3)/(5)}=25d^{(15)/(5)}=25d^3

Simplifying further


25d^3=25d^3

Step 2: substitute the value obtained above in step 1 into the parentheses, so that


((75d^(18\/5))/(3d^(3\/5)))^{(5)/(2)}=(25d^3)^{(5)/(2)}

Step 3: Simplify further, we will apply the rule

so that


(25d^3)^{(5)/(2)}=25^{(5)/(2)}d^{3*(5)/(2)}

Simplifying further


\begin{gathered} we\text{ will have} \\ √(25^5)* d^{(15)/(2)}=3125d^{(15)/(2)} \end{gathered}

Hence, our final answer is


3125d^{(15)/(2)}

Hello, is it possible to show me the steps to simplify this problem? I don't understand-example-1
Hello, is it possible to show me the steps to simplify this problem? I don't understand-example-2
User Andre Carrera
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