Question

I just need some guidance.. I know how to do each one individually

Answer 1

Given:

`(5a^2c^{-(1)/(2)}d^{(3)/(4)})^2`

Applying the properties of exponents:

`\begin{gathered} =(5)^2\text{ }*(c^{-(1)/(2)})^2\text{ }*(d^{(3)/(4)})^2 \\ =\text{ 25 }* c^{-(1)/(2)*2}\text{ }* d^{(3)/(4)*2} \\ =\text{ 25 }* c^{(-2)/(2)}* d^{(6)/(4)} \\ =\text{ 25 }* c^(-1)* d^{(3)/(2)} \end{gathered}`

Simplifying the powers:

`=\text{ 25 }* c^(-1)* d^{(3)/(2)}`

Writing exponents as positive integers:

`=\text{ }\frac{25d^{(3)/(2)}}{c}`

The result as a radical expression:

`=\text{ }\frac{25\sqrt[]{d^3}}{c}`